Systems and methods for handling sector gaps in inter-track interference compensation

ABSTRACT

Various embodiments of the present invention provide systems and methods for data processing. As an example, a data processing circuit is discussed that includes an inter-track interference determination circuit operable to calculate an inter-track interference from a previous track data set based at least in part on the previous track data set and a current track data set. The previous track data set includes a gap. A portion of the data in the previous track data set corresponds to a previous track on a storage medium, and the data in the previous track data set corresponding to the gap corresponds to a track preceding a previous track.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application claims priority to (is a non-provisional of)U.S. Pat. App. No. 61/453,676, entitled “Systems and Methods for Trackto Track Interference Compensation”, and filed Mar. 17, 2011 by Mathewet al.; U.S. Pat. App. No. 61/453,680, entitled “Systems and Methods forHandling Sector Gaps in Inter-track Interference Compensation”, andfiled Mar. 17, 2011 by Mathew et al.; U.S. Pat. App. No. 61/382,117,entitled “Estimation and Cancellation of ITI in SMR”, and filed Sep. 10,2010 by Mathew et al. The entirety of the aforementioned provisionalpatent application is incorporated herein by reference for all purposes.

BACKGROUND OF THE INVENTION

The present inventions are related to systems and methods for dataprocessing, and more particularly to systems and methods for processingdata retrieved from a storage medium.

Data storage systems often store data arranged in tracks. FIG. 1 a showsa storage medium 101 with two exemplary tracks 151,156 indicated asdashed lines. The tracks are segregated by servo data written withinwedges 161, 166 (i.e., servo wedges). These wedges include data andsupporting bit patterns 111 that are used for control andsynchronization of the read/write head assembly over a desired locationon storage medium 101. In particular, these wedges generally include apreamble pattern 192 followed by a sector address mark 194 (SAM). Sectoraddress mark 194 is followed by a Gray code 196, and Gray code 196 isfollowed by burst information 198. It should be noted that while twotracks and two wedges are shown, hundreds of each would typically beincluded on a given storage medium. User data is stored at bit periodlocations between successive servo wedges.

FIG. 1 b shows an existing track to track layout 100 of data on astorage medium. Of note, track to track layout 100 includes only some ofthe data across some of the tracks that would be expected on an existingstorage medium. As shown, layout 100 includes a number of tracks 105,110, 115, 120, 125. Each of the tracks includes a synchronizationpattern 150 (i.e., sync data 1, sync data 2, sync data 3, sync data 4,sync data 5) followed by bit periods of user data 155, 160, 165, 170,175, 180, 185, 190. The bit periods each include magnetic informationcorresponding to data for a given bit period. As the density of the bitperiods increase, magnetic information from one bit period willinterfere or be combined with magnetic information from surrounding bitperiods. This includes interaction from bit periods in one track withbit periods in prior and subsequent tracks. Failure to properly accountfor inter-track interference results in diminished accuracy of read backdata.

Hence, for at least the aforementioned reasons, there exists a need inthe art for advanced systems and methods for inter-track interferencecompensation.

BRIEF SUMMARY OF THE INVENTION

The present inventions are related to systems and methods for dataprocessing, and more particularly to systems and methods for processingdata retrieved from a storage medium.

Various embodiments of the present invention provide non-zero gap,inter-track interference compensation circuits. Such circuits include aninter-track interference determination circuit operable to calculate aninter-track interference from a previous track data set based at leastin part on the previous track data set and a current track data set. Theprevious track data set includes a gap. A portion of the data in theprevious track data set corresponds to a previous track on a storagemedium, and the data in the previous track data set corresponding to thegap corresponds to a track preceding a previous track. In some instancesof the aforementioned embodiments, the circuit further includes a databuffer and a hard data load circuit. The data buffer is operable tostore the portion of previous track data set. The hard data load circuitis operable determine a location of the gap and to load the previoustrack data set into the data buffer. In particular cases, the gap iswritten with data corresponding to the track preceding the previoustrack. In some cases, the circuit further includes an inter-trackinterference cancellation circuit that is operable to cancel theinter-track interference from the previous track data set to yield acompensated output.

In some cases, the gap is an unused area between a sync mark region anda user data region. In one or more cases, at least a portion of the userdata region is written with data corresponding to the track precedingthe previous track, and is overwritten with data corresponding to theprevious track. In various cases, at least a portion of the sync markregion is written with data corresponding to the track preceding theprevious track, and is overwritten with data corresponding to theprevious track. In one or more cases, at least a portion of the gap iswritten with data corresponding to the track preceding the previoustrack, and is not overwritten with data corresponding to the previoustrack.

In particular cases, the inter-track interference determination circuitincludes: an inter-track interference response circuit, and aninter-track interference signal estimator circuit. The inter-trackinterference response circuit is operable to estimate an inter-trackinterference response from the previous track data set based at least inpart on the previous track data set and a current track data set. Theinter-track interference signal estimator circuit operable to calculatean inter-track interference from the previous track data set based atleast in part on the previous track data set and the inter-trackinterference response from the previous track data set.

Other embodiments of the present invention provide methods forcancelling inter-track interference in a non-zero gap data set. Suchmethods include: receiving a current track data set derived from acurrent track on a storage medium; accessing a previous track data setthat was derived from a previous track on the storage medium, and theprevious track data set includes a gap having data that corresponds to atrack preceding the previous track on the storage medium; calculating anestimated inter-track interference response from the previous track dataset based at least in part on the current track data set and theprevious track data set; and calculating an inter-track interferencefrom the previous track data set based at least in part on the previoustrack data set and the inter-track interference response from theprevious track data set. In some cases, the methods further includecancelling the inter-track interference from the previous track data setto yield a compensated output.

In some cases, the gap is an unused area between a sync mark region anda user data region. In some cases, at least a portion of the user dataregion and at least a portion of the sync mark region are written withdata corresponding to the track preceding the previous track, and areoverwritten with data corresponding to the previous track, and at leasta portion of the gap is written with data corresponding to the trackpreceding the previous track, and is not overwritten with datacorresponding to the previous track.

Yet other embodiments of the present invention provide storage devices.The storage devices include: a storage medium, a read/write headassembly disposed in relation to the storage medium, and a read channelcircuit operable to receive an information set from the storage mediumvia the read/write head assembly. The read channel circuit includes: afront end circuit, a data buffer, a hard data load circuit, and aninter-track interference determination circuit. The front end circuit isoperable to convert the information set to a current track data set. Thehard data load circuit is operable determine a location of a gap in adata set derived from a previous track and to load a previous track dataset into the data buffer. The previous track data set includes datacorresponding to the previous track for locations other than thelocation of the gap and includes data from a track preceding theprevious track at the location of the gap. The inter-track interferencedetermination circuit is operable to calculate an inter-trackinterference from the previous track data set based at least in part onthe previous track data set and the current track data set.

In some instances of the aforementioned embodiments, the inter-trackinterference determination circuit includes: an inter-track interferenceresponse circuit and an inter-track interference signal estimatorcircuit. The inter-track interference response circuit is operable toestimate an inter-track interference response from the previous trackdata set based at least in part on the previous track data set and acurrent track data set. The inter-track interference signal estimatorcircuit is operable to calculate an inter-track interference from theprevious track data set based at least in part on the previous trackdata set and the inter-track interference response from the previoustrack data set. In various instances of the aforementioned embodiments,the read channel circuit further includes an inter-track interferencecancellation circuit operable to cancel the inter-track interferencefrom the previous track data set to yield a compensated output.

This summary provides only a general outline of some embodiments of theinvention. Many other objects, features, advantages and otherembodiments of the invention will become more fully apparent from thefollowing detailed description, the appended claims and the accompanyingdrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

A further understanding of the various embodiments of the presentinvention may be realized by reference to the figures which aredescribed in remaining portions of the specification. In the figures,like reference numerals are used throughout several figures to refer tosimilar components. In some instances, a sub-label consisting of a lowercase letter is associated with a reference numeral to denote one ofmultiple similar components. When reference is made to a referencenumeral without specification to an existing sub-label, it is intendedto refer to all such multiple similar components.

FIG. 1 a depicts an existing storage medium including servo data;

FIG. 1 b depicts an existing track to track layout of data on a storagemedium;

FIGS. 2 a-2 c depict example track to track layouts that may be operatedon in accordance with different embodiments of the present invention;

FIG. 3 depicts an inter-track interference compensation circuit inaccordance with one or more embodiments of the present invention;

FIG. 4 is a flow diagram showing a method for inter-track interferencecompensation using an adaptive inter-track interference responseestimation circuit in accordance with one or more embodiments of thepresent invention;

FIG. 5 depicts another inter-track interference compensation circuit inaccordance with other embodiments of the present invention;

FIG. 6 is a flow diagram showing a method for inter-track interferencecompensation using a correlation based inter-track interference responseestimation circuit in accordance with one or more embodiments of thepresent invention;

FIG. 7 depicts a non-zero frequency offset inter-track interferencecompensation circuit in accordance with one or more embodiments of thepresent invention;

FIG. 8 depicts a gap compensating inter-track interference cancellationcircuit in accordance with one or more embodiments of the presentinvention;

FIG. 9 is a flow diagram showing a shingled write approach that mayoccur in relation to various embodiments of the present invention;

FIG. 10 is a flow diagram showing a method in accordance with variousembodiments of the present invention for gap compensation in aninter-track interference cancellation approach;

FIG. 11 depicts a combination gap compensating and frequency offsetcompensating inter-track interference cancellation circuit in accordancewith some embodiments of the present invention;

FIG. 12 is a flow diagram showing a method in accordance with someembodiments of the present invention for block-wise gap compensation inan inter-track interference cancellation approach;

FIG. 13 depicts a data alignment based inter-track interferencecancellation circuit in accordance with some embodiments of the presentinvention;

FIG. 14 depicts an example track to track layout exhibiting substantialtrack to track offsets that may be operated on in accordance withdifferent embodiments of the present invention;

FIG. 15 is a flow diagram showing a method in accordance with someembodiments of the present invention for offset compensation in aninter-track interference cancellation approach; and

FIG. 16 shows a storage system with an inter-track interferencecompensation circuit in accordance with various embodiments of thepresent invention.

DETAILED DESCRIPTION OF THE INVENTION

The present inventions are related to systems and methods for dataprocessing, and more particularly to systems and methods for processingdata retrieved from a storage medium.

In a storage system where bit period density has increased to the pointthat interference from one bit period location to another bit periodlocation occurs, inter-track interference between bit periods insurrounding tracks may be estimated by correlating a read back signalfrom track being processed with hard data bits (i.e., non-return to zerodata bits) from an adjacent track. This process is less complex wherethe sectors across tracks are radially aligned from one track to thenext track, but becomes more complex where such alignment does notexist.

Various embodiments of the present invention provide for estimatinginter-track interference where the radial alignment of bit periods(i.e., data bits) between tracks is undermined due to a non-zero phaseoffset between tracks and/or sector gaps. Where, for example, radialalignment is offset due to write clock frequency offset between tracks,the radial mis-alignment increases as traversal in a down-trackdirection continues (i.e., as the distance between the synchronizationdata and the particular bit period increases). FIG. 2 a depicts a trackto track layout 200 where the phase offset between corresponding bitperiods in adjacent tracks is non-zero. As shown, two tracks 205, 210each begin with a respective sync data (i.e., sync data 1 and sync data2). A first bit period (i.e., bit 1,1) in track 205 begins at the samepoint as a first bit period (i.e., bit 2,1) in track 210, but endsearlier. In particular, a phase offset 290 exists between the end of bit1,1 and bit 2,1. The offset between bit periods increases as thedistance from the sync data increases. In particular, a phase offset 292is greater than phase offset 290; a phase offset 294 is greater thanphase offset 292; a phase offset 296 is greater than phase offset 294.Such a progressively increasing phase offset typically occurs due to afrequency mismatch between the write clock used to write the user datato track 205 and the write clock used to write the user data to track210. Of note, it is assumed that the phase offset is approximately zeronear the beginning of the user data period as indicated by the syncdata.

Because of the non-zero frequency offset between tracks, the actualinter-track interference compensation drifts along a time axis as datais processed from the beginning of a servo wedge to the end of a servowedge. Consequently, direct correlation of a read back signal from trackbeing processed with hard data from an adjacent track does not yield acorrect inter-track interference response if the correlation isperformed across an entire wedge (i.e., a user data region extendingbetween successive servo wedges). Some embodiments of the presentinvention that operate in such a non-zero phase offset environmentutilize a block-wise inter-track interference estimation andcancellation to account for the effect of write frequency offset (i.e.,the varying phase offset between adjacent tracks).

In one or more embodiments of the present invention, the block-wiseinter-track interference estimation and cancellation involves splittingdata within a given wedge so that the net phase change across a block ofbit periods across adjacent tracks is relatively small compared with alarger block. By maintaining the net phase change small, the use ofdirect correlation of adjacent bit periods may be used within thesub-block region. In some instances, the block size is on the order offive thousand (5000) bit periods.

Based on the relative shift of the estimated inter-track interferenceresponse from one block to another, a shifting strategy can beincorporated into the correlation process to account for the frequencyoffset. By selecting a block size that is relatively small when comparedwith, for example, entire tracks or wedges, the overall phase shiftwithin the selected block can be sufficiently small that interpolationand other more expensive methods are not required to account for thevarying phase shifts. Block size depends on the frequency offset, largersub-block sizes can be used where the frequency offset between adjacenttracks is small. In some cases, methods to estimate phase offsets causedby jitter in the write and read (e.g., the assertion of write gates andread gates) may be used in conjunction with the aforementioned processesfor inter-track interference estimation and compensation.

Turning to FIG. 2 b, a track to track layout 201 is shown where gapsoccur along the tracks. Some embodiments of the present provideprocessing to accommodate such gaps. Track to track layout 201 includesa number of tracks (Track N−2, Track N−1, Track N, Track N+1 and TrackN+2) arranged without radial alignment between the various fields. Inparticular, Track N−2 of the tracks is the first to be written withTrack N+2 being the last to be written. Track N−2 includes a user dataregion 260, a gap 262, a synchronization data region 264 (e.g., preambleand sync mark fields, a servo wedge, or both), a user data region 266and a gap 268; track N−1 includes a user data region 250, a gap 252, asynchronization data region 254, a user data region 256 and a gap 258;track N includes a gap 242, a synchronization data region 244, a userdata region 246, a gap 248, and a synchronization data region 249; trackN+1 includes a user data region 230, a gap 232, a synchronization dataregion 234, a user data region 236, a gap 238, and a synchronizationdata region 239; and track N+2 includes a user data region 220, a gap222, a synchronization data region 224, a user data region 226, a gap228, and a synchronization data region 229.

Shingled writing (writing over one selected track and an adjacent track,followed by re-writing the region on the adjacent track during asubsequent track write) of the tracks begins by writing track N−2.During this write, magnetic information corresponding to the write oftrack N−2 is also written to track N−1. When track N−1 is written thepreviously written magnetic information is overwritten except at thelocations of gap 252 and gap 258 where the previously written magneticinformation corresponding to track N−2 was written. Similarly, whenwriting track N−1, the magnetic information corresponding to the writeof track N−1 is also written to track N. When track N is written, thepreviously written magnetic information is overwritten except at thelocations of gap 242 and gap 248 where the previously written magneticinformation corresponding to track N−1 was written. This processcontinues until all of the tracks are written. As will be appreciated,most regions of a given track will include inter-track interferencepredictable based upon the tracks on either side of the track at issue.However, for the gap regions in the adjacent tracks, the inter-trackinterference will correspond to data that was written two tracks prior(e.g., for Track N, the inter-track interference corresponding to gap252 and gap 258 will be that written in the corresponding locations intrack N−2). Some embodiments of the present invention account for thisdistant interference.

In some embodiments of the present invention, accounting for suchdistant inter-track interference is rendered less complex by readingdata in the same direction as it was originally written to the storagemedium. Such common direction read and write operations is not requiredin all embodiments of the present invention, but does alleviate the needto buffer considerable data to store and re-order the data when the readis done in the opposite direction of the write. Inter-track interferencecaused by overlap with sector gaps in some cases is not cancelled as itis constructive in nature to the track to which the current read isdirected. Inter-track interference from sector gaps from previous tracksmay be canceled using the track preceding the previous track as thatdata can be made available. Residual inter-track interference from asubsequent track and other un-cancelled inter-track interference thatremains after inter-track interference cancellation of interference frompreceding tracks can be modeled as stationary zero-mean colored noisewhich is independent of the data from the track that is being read. Insome cases, a read head offset may be optimized to minimize inter-trackinterference from a subsequent track. In some cases, residualinter-track interference from sector gaps as well as other componentsbehaves like electronics noise, resulting in reducing the percentage ofmedia noise on target track. In such cases, use of an additional noiseprediction filter bank operates to reduce the impact of residualinter-track interference.

Some embodiments of the present invention address track-to-trackinterference related to gaps, by radially aligning any gaps. FIG. 2 cdepicts a track-to-track layout 271 where the gaps in the respectivetracks are radially aligned. Track to track layout 271 includes a numberof tracks (Track N−2, Track N−1, Track N, Track N+1 and Track N+2)arranged with radial alignment between corresponding fields or regionsof data. In particular, track N−2 of the tracks is the first to bewritten with track N+2 being the last to be written. Track N−2 includesa user data region 261, a gap 263, a synchronization data region 265(e.g., preamble and sync-mark fields, a servo wedge, or both), a userdata region 267 and a gap 269; track N−1 includes a user data region251, a gap 253, a synchronization data region 255, a user data region257 and a gap 259; track N includes a user data region 241, a gap 243, asynchronization data region 245, a user data region 247 and a gap 273;track N+1 includes a user data region 231, a gap 233, a synchronizationdata region 235 (e.g., a servo wedge), a user data region 237 and a gap275; and track N+2 includes a user data region 221, a gap 223, asynchronization data region 225, a user data region 227 and a gap 277.By assuring such radial alignment, the inter-track interferenceoccurring in the gaps can be largely ignored, except on the fringeswhere frequency offset between tracks can result in overlap of a gap anda user data region at the margins.

Turning to FIG. 3, an inter-track interference compensation circuit 300is shown in accordance with one or more embodiments of the presentinvention. Inter-track interference compensation circuit 300 receives ananalog input signal 377. Analog input signal 377 may be derived, forexample, from a read/write head assembly (not shown) disposed inrelation to a storage medium (not shown), and represents informationsensed from the storage medium. Analog input signal 377 is provided toan analog to digital converter circuit 380 that operates to convert theanalog signal into a series of digital samples 382 corresponding toanalog input signal 377. Analog to digital converter circuit 380 may beany circuit known in the art that is capable of converting an analogsignal into corresponding series of digital samples. Based upon thedisclosure provided herein, one of ordinary skill in the art willrecognize a variety of analog to digital converter circuits and/orarchitectures that may be used in relation to different embodiments ofthe present invention. Digital samples 382 are provided to an equalizercircuit 385 that equalizes the digital samples and provides an equalizedoutput 303 (r[n]) to an adaptive inter-track interference responseestimation circuit 320. In some embodiments of the present invention,equalizer circuit 385 may be implemented as a digital finite impulseresponse circuit as are known in the art. Based upon the disclosureprovided herein, one of ordinary skill in the art will recognize avariety of equalizer circuits and/or architectures that may be used inrelation to different embodiments of the present invention. Whereinter-track interference is not a concern (i.e., the tracks areseparated by substantial distance), continuous-time version of theequalized output 303 is represented by the following equation:r ₀ [t]=Σa ₀ [k]h ₀(t−kT),where a₀[k] represents the currently sensed bit period from the storagemedium, T denotes the duration of one bit, and h₀(t) represents theinter-symbol interference function (i.e., interference from adjacentsymbols along the same track). The inter-track interferencecorresponding to the two tracks on either side of the current track inequalized output 303 (i.e., an inter-track interference from a previoustrack r⁻¹(t), and an inter-track interference from a next track r₁(t))may be represented by the following equations, respectively:r ⁻¹(t)=Σa ⁻¹ [k]h ⁻¹(t−kT+τ ⁻¹)andr ₁(t)=Σa ₁ [k]h ₁(t−kT+τ ₁),where h⁻¹(t) represents the inter-track interference response from theprevious track, h₁(t) represents the inter-track interference responsefrom the next track, τ⁻¹ represents the phase delay of the track beingread with respect to the previous track, and τ₁ represents the phasedelay of the track being read with respect to the next track. Thefunctions h⁻¹(.) and h₁(.) are interference models based on variouscriteria including the relative proximity of adjacent tracks. Suchmodels may be developed for a particular storage device or medium.Accounting for the inter-track interference, equalized output 303 (incontinuous-time) may be represented by the following equation:r(t)=r ₀(t)+r ₁(t)+r ⁻¹(t).Thus, discrete-time version of the equalized output 303 may berepresented by the following equation:r[n]=r(nT)=Σa ₀ [k]g ₀ [n−k]+Σa ₁ [k]g ₁ [n−k]+Σa ⁻¹ [k]g ⁻¹ [n−k],where g₀[k]=h₀(kT), g₁[k]=h₁(kT+τ₁), and g⁻¹[k]=h⁻¹(kT+τ⁻¹). Assuming{a₀[n], a⁻¹[n], a₁[n]} are mutually uncorrelated bit streams, theexpected values for the functions h⁻¹(.) and h₁(.) are defined asfollows:E[r[n]·a ⁻¹ [n−n ⁻¹ ]]=g ⁻¹ [n ⁻¹ ]=h ⁻¹(n ⁻¹ T+{circumflex over (τ)}⁻¹);andE[r[n]·a ₁ [n−n ₁ ]]=g ⁻¹ [n ₁ ]=h ₁(n ₁ T+{circumflex over (τ)} ₁),respectively.

Inter-track interference compensation circuit 300 includes a buffer 310that stores hard data bits retrieved from a previous track (i.e., atrack located on a first side of the track being processed), and abuffer 315 that stores hard data bits retrieved from a next track (i.e.,a track located on a second side of the track being processed). Thesehard bits may be stored after a prior processing of data sensed from therespective tracks (i.e., the previous track and the next track). Thedata from buffer 310 is provided as a data output 312 and is denoted asa⁻¹[n], where n indicates the bit position within the track. The datafrom buffer 315 is provided as a data output 314 and is denoted asa₁[n], where n indicates the bit position within the track. Data input312 and data input 314 are provided to adaptive inter-track interferenceresponse estimation circuit 320 and an inter-track interferenceestimator circuit 325.

Latency circuit 335 delays equalized output 303 in time to match thelatency involved in calculating inter-track interference responses byinter-track interference estimator circuit 320 and in calculatinginter-track interference by inter-track interference estimator circuit325. The delayed signals are provided as a delayed output 337 to aninter-track interference cancellation circuit 330.

Adaptive inter-track interference response estimation circuit 320calculates an estimated inter-track interference response from theprevious track (ĝ⁻¹[k,n+1]) and provides it as a previous trackinterference output 322. Previous track interference response 322 iscalculated in accordance with the following equation:ĝ ⁻¹ [k,n+1]=ĝ ⁻¹ [k,n]+μ ⁻¹ a ⁻¹ [n−k]·[r[n]−{tilde over (r)} ⁻¹ [n]]),where {tilde over (r)}⁻¹[n] is the inter-track interference from aprevious track provided as an output 362 to a summation circuit 360, andcorresponds to the following equation:

${{\overset{\sim}{r}}_{- 1}\lbrack n\rbrack} = {\sum\limits_{k = {- M_{- 1}}}^{k = M_{- 1}}{{{\hat{g}}_{- 1}\left\lbrack {k,n} \right\rbrack}{{a_{- 1}\left\lbrack {n - k} \right\rbrack}.}}}$The value of [r[n]−{tilde over (r)}⁻¹[n]] is provided as an output 364from summation circuit 360, and a⁻¹ [n−k] is the preceding hard decisionfrom buffer 310. Similarly, adaptive inter-track interference responsecircuit 320 calculates an estimated inter-track interference responsefrom the next track (ĝ₁[k,n+1]) and provides it as a next trackinterference response 324.ĝ ₁ [k,n+1]=ĝ ₁ [k,n]+μ ₁ a ₁ [n−k]·[r[n]−{tilde over (r)} ₁ [n]]),where {tilde over (r)}₁[n] is the inter-track interference from a nexttrack provided as an output 372 to a summation circuit 370, andcorresponds to the following equation:

${{\overset{\sim}{r}}_{1}\lbrack n\rbrack} = {\sum\limits_{k = {- M_{1}}}^{k = M_{1}}{{{\hat{g}}_{1}\left\lbrack {k,n} \right\rbrack}{{a_{1}\left\lbrack {n - k} \right\rbrack}.}}}$The value of [r[n]−{tilde over (r)}₁[n]] is provided as an output 374from summation circuit 370, and a₁[n−k] is the succeeding hard decisionfrom buffer 315. In some cases, the estimated outputs may be estimatedusing a correlation approach, rather than by direct computation asdiscussed below in relation to FIG. 5.

Next track interference response 324 and previous track interferenceresponse 322 are provided to inter-track interference estimator circuit325. Inter-track interference estimator circuit 325 estimates theinter-track interference from the previous track ({{circumflex over(r)}⁻¹[n]}) and provides it as a previous track interference output 327.Previous track interference output 327 is estimated (i.e., calculated)in accordance with the following equation:{circumflex over (r)} ⁻¹ [n]=Σa ⁻¹ [n−k]ĝ ⁻¹ [k],across the bit periods for the track. Similarly, inter-trackinterference estimator circuit 325 estimates the inter-trackinterference from the next track ({{circumflex over (r)}₁[n]}) for thebit periods and provides it as a next track interference output 329.Next track interference output 329 is estimated (i.e., calculated) inaccordance with the following equation:{circumflex over (r)} ₁ [n]=Σa ₁ [n−k]ĝ ₁ [k],across the bit periods included in the track.

Next track interference output 329 and previous track interferenceoutput 327 are provided to inter-track interference cancellation circuit330. Inter-track interference cancellation circuit 330 subtracts theinter-track interference signals from the delayed output to yield aninter-track track interference compensated output 332 ({{circumflex over(r)}₀[n]}), across the bit periods included in the track. Inter-trackinterference compensated output 332 is calculated in accordance with thefollowing equation:{circumflex over (r)} ₀ [n]=r[n]−{circumflex over (r)} ₁ [n]−{circumflexover (r)} ⁻¹ [n],across the bit periods included in the track. It should be noted thatwhile the approach discussed in relation to inter-track interferencecompensation circuit 300 cancels inter-track interference from both aprevious and a next track, the approach may be simplified to cancelinter-track interference from only one of the previous track or the nexttrack. In one case, single sided inter-track interference compensationmay be used for real time (e.g., while a storage device is beingaccessed) operation of the circuit, while double sided inter-trackinterference compensation may be used for off time (e.g., while anattempt to recover data that was not recoverable in real time isperformed) operation of the circuit.

Turning to FIG. 4, a flow diagram 400 shows a method for inter-trackinterference compensation using an adaptive inter-track interferenceresponse estimation circuit in accordance with one or more embodimentsof the present invention. Following flow diagram 400, a track to be readis selected (block 405). In cases where both the previous track and thenext track are to be considered in cancelling inter-track interference,the hard data (i.e. data bits) corresponding to the next track and theprevious track have been loaded into respective inter-track interferencebuffers. Thus, for example, where track N is selected for reading, asucceeding track inter-track interference buffer holding the hard datacorresponding to the track N+1 is loaded, and the data corresponding totrack N−1 for the regions of user data region 250, synchronization data254 and user data region 256, and the data from track N−2 correspondingto gap 252 (i.e., a portion of gap 262 and a subsequent portion ofsynchronization data 264) and gap 258 (i.e., a portion of gap 268 and asubsequent portion of track N−2) is loaded into a preceding trackinter-track interference buffer. It should be noted that the approachdiscussed in relation to FIG. 4 may be modified to allow for partialinter-track interference cancellation using only one side of the data.In such a case, the hard data corresponding only to the previous trackhave been loaded into the inter-track interference buffer correspondingto the previous track.

A read/write head assembly is positioned relative to the selected trackand it is determined whether the servo wedge data has been identified(block 410). Once the servo wedge data has been found and processed(block 410), data is read from the selected track and stored as currentread data to a current read data buffer (bock 415). Inter-trackinterference cancellation using an adaptive inter-track interferenceresponse estimation circuit is performed on the current read data usingthe preceding track inter-track interference buffer and the succeedingtrack inter-track interference buffer to yield inter-track interferencecanceled data (block 435). Such inter-track interference cancellationmay be done consistent with that described above in relation to FIG. 3.This inter-track interference canceled data is provided to a downstreamdata processing circuit to yield hard data corresponding to the selectedtrack (block 440). Such downstream processing may be any processingcircuit known in the art. In one particular embodiment of the presentinvention, the downstream processing may include performing one or moreiterations of a combination of a maximum a posteriori data detectionprocess and a low density parity check decoding process. Based on thedisclosure provided herein, one of ordinary skill in the art willrecognize various processing circuits and approaches that may be used inaccordance with different embodiments of the present invention to yieldhard data from the inter-track interference canceled data.

As the hard data corresponding to the selected track become available itis determined whether the bits correspond to a gap in the current track(block 445). Thus, using the example of FIG. 2 b, it is determinedwhether the hard data for the current track (e.g., track N) correspondsto gap 242 or gap 248. Where the hard data does not correspond to a gap(block 445), the current read data is stored to the preceding trackinter-track interference buffer (block 450). Otherwise, where the harddata correspond to a gap (block 445), the prior value in the precedingtrack inter-track interference buffer remains as it is not overwrittenby the current data. Thus, using the example of FIG. 2 b where thecurrent track is track N, data from a portion of user data region 250 oftrack N−1 corresponding to gap 242 and data from a portion of user dataregion 256 of track N−1 corresponding to gap 248 remain in the precedingtrack inter-track interference buffer.

The next bit period is then selected (block 455). It is determined ifthe end of the wedge (i.e., the region between servo data wedges) hasbeen reached (block 460). Where the end of the wedge has not yet beenreached (block 460), the processes of blocks 415-460 is repeated for thenext bit period. Alternatively, where the end of the wedge has beenreached (block 460), it is determined whether the end of the track hasbeen reached (block 465). Where the end of the track has not yet beenreached (block 465), the processes of blocks 410-465 are repeated forthe remaining portion of the current track. Otherwise, the next track isselected and the processes of blocks 410-465 are repeated for the nexttrack. By following this approach, the preceding track inter-trackinterference buffer is prepared for processing the next track when aconsecutive track read is followed by including data from a trackpreceding the preceding track that corresponds to gaps in the precedingtrack.

Turning to FIG. 5, an inter-track interference compensation circuit 500is shown in accordance with one or more embodiments of the presentinvention. Inter-track interference compensation circuit 500 receives ananalog input signal 577. Analog input signal 577 may be derived, forexample, from a read/write head assembly (not shown) disposed inrelation to a storage medium (not shown), and represents informationsensed from the storage medium. Analog input signal 577 is provided toan analog to digital converter circuit 580 that operates to convert theanalog signal into a series of digital samples 582 corresponding toanalog input signal 577. Analog to digital converter circuit 580 may beany circuit known in the art that is capable of converting an analogsignal into corresponding series of digital samples. Based upon thedisclosure provided herein, one of ordinary skill in the art willrecognize a variety of analog to digital converter circuits and/orarchitectures that may be used in relation to different embodiments ofthe present invention. Digital samples 582 are provided to an equalizercircuit 585 that equalizes the digital samples and provides an equalizedoutput 503 (r[n]) to a correlation based inter-track interferenceresponse estimation circuit 520. In some embodiments of the presentinvention, equalizer circuit 585 may be implemented as a digital finiteimpulse response circuit as are known in the art. Based upon thedisclosure provided herein, one of ordinary skill in the art willrecognize a variety of equalizer circuits and/or architectures that maybe used in relation to different embodiments of the present invention.Where inter-track interference is not a concern (i.e., the tracks areseparated by substantial distance), continuous-time version of theequalized output 503 is represented by the following equation:r ₀ [t]=Σa ₀ [k]h ₀(t−kT),where a₀[k] represents the currently sensed bit period from the storagemedium, T denotes the duration of one bit, and h₀(t) represents theinter-symbol interference function (i.e., interference from adjacentsymbols along the same track). The inter-track interferencecorresponding to the two tracks on either side of the current track inequalized output 503 (i.e., an inter-track interference from a previoustrack r⁻¹(t), and an inter-track interference from a next track r₁(t))may be represented by the following equations, respectively:r ⁻¹(t)=Σa ⁻¹ [k]h ⁻¹(t−kT+τ ⁻¹)andr ₁(t)=Σa ₁ [k]h ₁(t−kT+τ ₁),where h⁻¹(t) represents the inter-track interference response from theprevious track, h₁(t) represents the inter-track interference responsefrom the next track, τ⁻¹ represents the phase delay of the track beingread with respect to the previous track, and τ₁ represents the phasedelay of the track being read with respect to the next track. Thefunctions h⁻¹(.) and h₁(.) are interference models based on variouscriteria including the relative proximity of adjacent tracks. Suchmodels may be developed for a particular storage device or medium.Accounting for the inter-track interference, equalized output 503 (incontinuous-time) may be represented by the following equation:r(t)=r ₀(t)+r ₁(t)+r ⁻¹(t).Thus, discrete-time version of the equalized output 503 may berepresented by the following equation:r[n]=r(nT)=Σa ₀ [k]g ₀ [n−k]+Σa ₁ [k]g ₁ [n−k]+Σa ⁻¹ [k]g ⁻¹ [n−k],where g₀[k]=h₀(kT), g₁[k]=h₁(kT+τ₁), and g⁻¹[k]=h⁻¹(kT+τ⁻¹). Assuming{a₀[n], a⁻¹ [n], a₁[n]} are mutually uncorrelated bit streams, theexpected values for the functions h⁻¹(.) and h₁(.) are defined asfollows:E[r[n]·a ⁻¹ [n−n ⁻¹ ]]=g ⁻¹ [n ⁻¹ ]=h ⁻¹(n ⁻¹ T+{circumflex over (τ)}⁻¹);andE[r[n]·a ₁ [n−n ₁ ]]=g ⁻¹ [n ₁ ]=h ₁(n ₁ T+{circumflex over (τ)} ₁),respectively.

Latency circuit 535 delays equalized output 503 in time to match thelatency involved in calculating inter-track interference responses byinter-track interference estimator circuit 520 and in calculatinginter-track interference by inter-track interference estimator circuit525. The delayed signals are provided as a delayed output 537 to aninter-track interference cancellation circuit 530.

Inter-track interference compensation circuit 500 includes a buffer 510that stores hard data bits retrieved from a previous track (i.e., atrack located on a first side of the track being processed), and abuffer 515 that stores hard data bits retrieved from a next track (i.e.,a track located on a second side of the track being processed). Thesehard bits may be stored after a prior processing of data sensed from therespective tracks (i.e., the previous track and the next track). Thedata from buffer 510 is provided as a data output 512 and is denoted asa⁻¹[n], where n indicates the bit position within the track. The datafrom buffer 515 is provided as a data output 514 and is denoted asa₁[n], where n indicates the bit position within the track. Data input512 and data input 514 are provided to correlation based inter-trackinterference response circuit 520 and an inter-track interferenceestimator circuit 525.

Correlation based inter-track interference response circuit 520calculates an estimated inter-track interference response from theprevious track (ĝ⁻¹[k]) and provides it as a previous track interferenceoutput 522. Previous track interference response 522 satisfies thefollowing equation:

${{{\hat{g}}_{- 1}\lbrack k\rbrack} = {\frac{1}{N_{- 1}}{\sum\limits_{n = 1}^{N_{- 1}}{{a_{- 1}\left\lbrack {n - k} \right\rbrack} \cdot {r\lbrack n\rbrack}}}}},$where N⁻¹ is the number of data bits available from a previous track,and a⁻¹ [n] are corresponding bits from a previous track. Similarly,correlation based inter-track interference response circuit 520 providesan estimated inter-track interference response from the next track(ĝ₁[k]) that satisfies the following equation:

${{{\hat{g}}_{1}\lbrack k\rbrack} = {\frac{1}{N_{1}}{\sum\limits_{n = 1}^{N_{1}}{{a_{1}\left\lbrack {n - k} \right\rbrack} \cdot {r\lbrack n\rbrack}}}}},$where N₁ is the number of data bits available from a next track, anda₁[n] are corresponding bits from a next track.

Next track interference response 524 and previous track interferenceresponse 522 are provided to inter-track interference estimator circuit525. Inter-track interference estimator circuit 525 estimates theinter-track interference from the previous track ({{circumflex over(r)}⁻¹[n]}) for the track and provides it as a previous trackinterference output 527. Previous track interference output 527 isestimated (i.e., calculated) in accordance with the following equation:{circumflex over (r)} ⁻¹ [n]=Σa ⁻¹ [n−k]ĝ ⁻¹ [k],across the bit periods for the track. Similarly, inter-trackinterference estimator circuit 525 estimates the inter-trackinterference from the next track ({{circumflex over (r)}₁[n]}) for thebit periods and provides it as a next track interference output 529.Next track interference output 529 is estimated (i.e., calculated) inaccordance with the following equation:{circumflex over (r)} ₁ [n]=Σa ₁ [n−k]ĝ ₁ [k],across the bit periods included in the track.

Next track interference output 529 and previous track interferenceoutput 527 are provided to inter-track interference cancellation circuit530. Inter-track interference cancellation circuit 330 subtracts theinter-track interference signals from the delayed output to yield aninter-track interference compensated output 532 ({{circumflex over(r)}₀[n]}), across the bit periods included in the track. Inter-trackinterference compensated output 532 is calculated in accordance with thefollowing equation:{circumflex over (r)} ₀ [n]=r[n]−{circumflex over (r)} ₁ [n]−{circumflexover (r)} ⁻¹ [n],across the bit periods included in the track. It should be noted thatwhile the approach discussed in relation to inter-track interferencecompensation circuit 500 cancels inter-track interference from both aprevious and a next track, the that approach may be simplified to cancelinter-track interference from only one of the previous track or the nexttrack. In one case, single sided inter-track interference compensationmay be used for real time (e.g., while a storage device is beingaccessed) operation of the circuit, while double sided inter-trackinterference compensation may be used for off time (e.g., while anattempt to recover data that was not recoverable in real time isperformed) operation of the circuit.

Turning to FIG. 6, a flow diagram 600 shows a method for inter-trackinterference compensation using a correlation based inter-trackinterference response estimation circuit in accordance with one or moreembodiments of the present invention. Following flow diagram 600, atrack to be read is selected (block 605). In cases where both theprevious track and the next track are to be considered in cancellinginter-track interference, the hard data corresponding to the next trackand the previous track have been loaded into respective inter-trackinterference buffers. Thus, for example, where track N is selected forreading, a succeeding track inter-track interference buffer holding thehard data corresponding to the track N+1 is loaded, and the datacorresponding to track N−1 for the regions of user data region 250,synchronization data 254 and user data region 256, and the data fromtrack N−2 corresponding to gap 252 (i.e., a portion of gap 262 and asubsequent portion of synchronization data 264) and gap 258 (i.e., aportion of gap 268 and a subsequent portion of track N−2) is loaded intoa preceding track inter-track interference buffer. It should be notedthat the approach discussed in relation to FIG. 6 may be modified toallow for partial inter-track interference cancellation using only oneside of the data. In such a case, the hard data corresponding only tothe previous track have been loaded into the inter-track interferencebuffer corresponding to the previous track.

A read/write head assembly is positioned relative to the selected trackand it is determined whether the servo wedge data has been identified(block 610). Once the servo wedge data has been found and processed(block 610), data is read from the selected track and stored as currentread data to a current read data buffer (bock 615). Inter-trackinterference cancellation using a correlation based inter-trackinterference response estimation circuit is performed on the currentread data using the preceding track inter-track interference buffer andthe succeeding track inter-track interference buffer to yieldinter-track interference canceled data (block 635). Such inter-trackinterference cancellation may be done consistent with that describedabove in relation to FIG. 5. This inter-track interference canceled datais provided to a downstream data processing circuit to yield hard datacorresponding to the selected track (block 640). Such downstreamprocessing may be any processing circuit known in the art. In oneparticular embodiment of the present invention, the downstreamprocessing may include performing one or more iterations of acombination of a maximum a posteriori data detection process and a lowdensity parity check decoding process. Based on the disclosure providedherein, one of ordinary skill in the art will recognize variousprocessing circuits and approaches that may be used in accordance withdifferent embodiments of the present invention to yield hard data fromthe inter-track interference canceled data.

As the hard data corresponding to the selected track become available itis determined whether the bits correspond to a gap in the current track(block 645). Thus, using the example of FIG. 2 b, it is determinedwhether the hard data for the current track (e.g., track N) correspondsto gap 242 or gap 248. Where the hard data does not correspond to a gap(block 645), the current read data is stored to the preceding trackinter-track interference buffer (block 650). Otherwise, where the harddata correspond to a gap (block 645), the prior value in the precedingtrack inter-track interference buffer remains as it is not overwrittenby the current data. Thus, using the example of FIG. 2 b where thecurrent track is track N, data from a portion of user data region 250 oftrack N−1 corresponding to gap 242 and data from a portion of user dataregion 256 of track N−1 corresponding to gap 248 remain in the precedingtrack inter-track interference buffer.

The next bit period is then selected (block 655). It is determined ifthe end of the wedge (i.e., the region between servo data wedges) hasbeen reached (block 660). Where the end of the wedge has not yet beenreached (block 660), the processes of blocks 615-660 is repeated for thenext bit period. Alternatively, where the end of the wedge has beenreached (block 660), it is determined whether the end of the track hasbeen reached (block 665). Where the end of the track has not yet beenreached (block 665), the processes of blocks 610-665 are repeated forthe remaining portion of the current track. Otherwise, the next track isselected and the processes of blocks 610-665 are repeated for the nexttrack. By following this approach, the preceding track inter-trackinterference buffer is prepared for processing the next track when aconsecutive track read is followed by including data from a trackpreceding the preceding track that corresponds to gaps in the precedingtrack.

Turning to FIG. 7, a non-zero frequency offset inter-track interferencecompensation circuit 700 is shown in accordance with one or moreembodiments of the present invention. Non-zero frequency offsetinter-track interference compensation circuit 700 receives an analoginput signal 777. Analog input signal 777 may be derived, for example,from a read/write head assembly (not shown) disposed in relation to astorage medium (not shown), and represents information sensed from thestorage medium. Analog input signal 777 is provided to an analog todigital converter circuit 780 that operates to convert the analog signalinto a series of digital samples 782 corresponding to analog inputsignal 777. Analog to digital converter circuit 780 may be any circuitknown in the art that is capable of converting an analog signal intocorresponding series of digital samples. Based upon the disclosureprovided herein, one of ordinary skill in the art will recognize avariety of analog to digital converter circuits and/or architecturesthat may be used in relation to different embodiments of the presentinvention. Digital samples 782 are provided to an equalizer circuit 785that equalizes the digital samples and provides an equalized output 703(r[n]) to a block selector circuit 705. In some embodiments of thepresent invention, equalizer circuit 785 may be implemented as a digitalfinite impulse response circuit as are known in the art. Based upon thedisclosure provided herein, one of ordinary skill in the art willrecognize a variety of equalizer circuits and/or architectures that maybe used in relation to different embodiments of the present invention.Where inter-track interference is not a concern (i.e., the tracks areseparated by substantial distance), continuous-time version of theequalized output 703 is represented by the following equation:r ₀ [t]=Σa ₀ [k]h ₀(t−kT),where a₀[k] represents the currently sensed bit period from the storagemedium, T denotes the duration of one bit, and h₀(t) represents theinter-symbol interference function (i.e., interference from adjacentsymbols along the same track). The inter-track interferencecorresponding to the two tracks on either side of the current track inequalized output 703 (i.e., an inter-track interference from a previoustrack r⁻¹ (t), and an inter-track interference from a next track r₁(t))may be represented by the following equations, respectively:r ⁻¹(t)=Σa ⁻¹ [k]h ⁻¹(t−kT+τ ⁻¹)andr ₁(t)=Σa ₁ [k]h ₁(t−kT+τ ₁),where h⁻¹(t) represents the inter-track interference response from theprevious track, h₁(t) represents the inter-track interference responsefrom the next track, τ⁻¹ represents the phase delay of the track beingread with respect to the previous track, and τ₁ represents the phasedelay of the track being read with respect to the next track. Thefunctions h⁻¹(.) and h₁(.) are interference models based on variouscriteria including the relative proximity of adjacent tracks. Suchmodels may be developed for a particular storage device or medium.Accounting for the inter-track interference, equalized output 703 (incontinuous-time) may be represented by the following equation:r(t)=r ₀(t)+r ₁(t)+r ⁻¹(t).Thus, discrete-time version of the equalized output 703 may berepresented by the following equation:r[n]=r(nT)=Σa ₀ [k]g ₀ [n−k]+Σa ₁ [k]g ₁ [n−k]+Σa ⁻¹ [k]g ⁻¹ [n−k],where g₀[k]=h₀(kT), g₁[k]=h₁(kT+τ₁), and g⁻¹[k]=h⁻¹(kT+τ⁻¹).

Non-zero frequency offset inter-track interference compensation circuit700 includes a buffer 710 that stores hard data bits retrieved from aprevious track (i.e., a track located on a first side of the track beingprocessed), and a buffer 715 that stores hard data bits retrieved from anext track (i.e., a track located on a second side of the track beingprocessed). These hard bits may be stored after a prior processing ofdata sensed from the respective tracks (i.e., the previous track and thenext track). The data from buffer 710 is provided as a data output 712and is denoted as a⁻¹[n], where n indicates the bit position within thetrack. The data from buffer 715 is provided as a data output 714 and isdenoted as a₁[n], where n indicated the bit position within the track.Data input 712 and data input 714 are provided to a block-wiseestimation of inter-track interference response circuit 720 and aninter-track interference estimator circuit 725.

A block selector circuit 705 identifies a block 707 of bit periods{r_(m)[n]} over which inter-track interference compensation is to beperformed, where m indicates the particular block that is selected and nindicates a given bit period along a track within the block. In somecases, the block size may be indicated as a letter i−1. In such cases,the value of n would extend from the first bit period in the selectedblock to the first bit period plus i. Thus, for example, if the firstbit period in the selected block is j, the block would include r[n],a₁[n] and a⁻¹[n] where n extends between j and i+j−1. The size of theblock selected may be predetermined and based upon a certain maximumfrequency error and/or jitter expected between adjacent tracks, or maybe variable and calculated based upon the estimated phase offset acrossa given number of sequential bit periods. Based upon the disclosureprovided herein, one of ordinary skill in the art will recognize avariety of block sizes that may be used in relation to differentembodiments of the present invention. Block 707 is provided toblock-wise estimation of inter-track interference response circuit 720,and to a block latency circuit 735.

Block latency circuit 735 delays block 707 in time to match the latencyinvolved in calculating inter-track interference responses by block-wiseestimation of inter-track interference response circuit 720 and incalculating inter-track interference by inter-track interferenceestimator circuit 725. The delayed signals are provided as a delayedoutput 737 to an inter-track interference cancellation circuit 730.

A block-to-block shift estimation of inter-track interference responsecircuit 740 calculates a phase delay 742 of the track being read withrespect to the previous track, and a phase delay 744 of the track beingread with respect to the next track. This calculation is done bydetermining the indices of the maximum tap coefficients in the estimatedinter-track interference responses that was used in generating previoustrack interference output 727 and next track interference output 729.Where the maximum filter tap of the inter-track interference responseused in calculating a respective one of previous track interferenceoutput 727 is one of the taps to the right of center or the left ofcenter in block-wise estimation of inter-track interference responsecircuit 720, then phase delay 742 is selected to cause a shift of themaximum tap back toward the center of the filter. Similarly, where themaximum filter tap of the inter-track interference response used incalculating a respective one of next track interference output 729 isone of the taps to the right of center or the left of center inblock-wise estimation of inter-track interference response circuit 720,then phase delay 744 is selected to cause a shift of the maximum tapback toward the center of the filter. Phase delay 742 and phase delay744 are provided along with data output 712, data output 714 and block707 to block-wise estimation of inter-track interference responsecircuit 720.

Block-wise estimation of inter-track interference response circuit 720calculates an estimated inter-track interference response from theprevious track (ĝ_(−1,m)[k]) and provides it as a previous trackinterference output 722. Previous track interference response 722satisfies the following equation:

${{\hat{g}}_{{- 1},m}\lbrack k\rbrack} = {\frac{1}{N_{- 1}}{\sum\limits_{n = 1}^{N_{- 1}}{{a_{- 1}\left\lbrack {n + {\left( {m - 1} \right)N_{b}} - k - \delta_{{- 1},m}} \right\rbrack} \cdot {r\left\lbrack {n + {\left( {m - 1} \right)N_{b}}} \right\rbrack}}}}$     δ_(−1, m) = δ_(−1, m − 1) + k_(−1, m − 1)where δ_(−1,m) denotes the shift in correlator reference required forcentering the inter-track interference response from the previous trackĝ_(−1,m)[k], N_(b) denotes the block-size, and k_(−1,m−1) denotes indexof the maximum tap coefficient in ĝ_(−1,m−1)[k]. In some cases, theestimated outputs may be estimated using an adaptive approach, ratherthan by correlation computation. Similarly, block-wise estimation ofinter-track interference response circuit 720 calculates an estimatedinter-track interference response from the next track (ĝ_(1,m)[k]) andprovides it as a next track interference response 724. Next trackinterference response 724 is calculated in accordance with the followingequation:

${{\hat{g}}_{1,m}\lbrack k\rbrack} = {\frac{1}{N_{1}}{\sum\limits_{n = 1}^{N_{- 1}}{{a_{1}\left\lbrack {n + {\left( {m - 1} \right)N_{b}} - k - \delta_{1,m}} \right\rbrack} \cdot {r\left\lbrack {n + {\left( {m - 1} \right)N_{b}}} \right\rbrack}}}}$     δ_(1, m) = δ_(1, m − 1) + k_(1, m − 1)where δ_(1,m) denotes the shift in correlator reference required forcentering the inter-track interference response from the previous trackĝ_(1,m)[k] and k_(1,m−1) denotes index of the maximum tap coefficient inĝ_(1,m−1)[k]. Starting phase offsets δ_(−1,0) and δ_(1,0) areinitialized to zero, if sectors are phase synchronized at the beginningand/or if no a priori information on phase offset is available.

Next track interference response 724 and previous track interferenceresponse 722 are provided to inter-track interference estimator circuit725. Inter-track interference estimator circuit 725 estimates theinter-track interference from the previous track ({{circumflex over(r)}_(−1,m)[n]}) for the block m and provides it as a previous trackinterference output 727. Previous track interference output 727 isestimated (i.e., calculated) in accordance with the following equation:{circumflex over (r)} _(−1,m) [n]=Σa ⁻¹ [n+(m−1)N _(b) −k−δ _(−1,m) ]ĝ_(−1,m) [k],across the bit periods included in the block m. Similarly, inter-trackinterference estimator circuit 725 estimates the inter-trackinterference from the next track ({{circumflex over (r)}_(1,m)[n]}) forthe block m and provides it as a next track interference output 729.Next track interference output 729 is estimated (i.e., calculated) inaccordance with the following equation:{circumflex over (r)} _(1,m) [n]=Σa ₁ [n+(m−1)N _(b) −k−δ _(1,m) ]ĝ_(1,m) [k],across the bit periods included in the block m.

Next track interference output 729 and previous track interferenceoutput 727 are provided to inter-track interference cancellation circuit730 along with delayed output 737. Inter-track interference cancellationcircuit 730 subtracts the inter-track interference signals from thedelayed output to yield an inter-track interference compensated output732 ({{circumflex over (r)}_(0,m)[n]}), across the bit periods includedin the block m. Inter-track interference compensated output 732 iscalculated in accordance with the following equation:{circumflex over (r)} _(0,m) [n]=r _(m) [n]−{circumflex over (r)} _(1,m)[n]−{circumflex over (r)} _(−1,m) [n],across the bit periods included in the block m.

As just some of many advantages achievable through use of a block-wiseinter-track interference estimation and cancellation circuitry:inter-track interference can be compensated using less circuitry thanmay be required if a digital phase locked loop and interpolationtechniques are used to compensate the frequency offset between writeclocks on adjacent tracks. Based upon the disclosure provided herein,one of ordinary skill in the art will recognize a variety of otheradvantages that may be achieved in accordance with various embodimentsof the present invention. Also, it should be noted that while thepreceding discussion applies inter-track interference processing to theoutput of an equalizer, such inter-track interference may also beapplied to other data outputs. For example, such inter-trackinterference processing may be applied to the output of the analog todigital converter.

FIG. 8 depicts a gap compensating inter-track interference cancellationcircuit 800 in accordance with one or more embodiments of the presentinvention. Gap compensating inter-track interference cancellationcircuit 800 receives an analog input signal 877. Analog input signal 877may be derived, for example, from a read/write head assembly (not shown)disposed in relation to a storage medium (not shown), and representsinformation sensed from the storage medium. Analog input signal 877 isprovided to an analog to digital converter circuit 880 that operates toconvert the analog signal into a series of digital samples 882corresponding to analog input signal 877. Analog to digital convertercircuit 880 may be any circuit known in the art that is capable ofconverting an analog signal into corresponding series of digitalsamples. Based upon the disclosure provided herein, one of ordinaryskill in the art will recognize a variety of analog to digital convertercircuits and/or architectures that may be used in relation to differentembodiments of the present invention. Digital samples 882 are providedto an equalizer circuit 885 that equalizes the digital samples andprovides an equalized output 803 (r[n]) to an inter-track interferenceresponse estimator circuit 820. In some embodiments of the presentinvention, equalizer circuit 885 may be implemented as a digital finiteimpulse response circuit as are known in the art. Based upon thedisclosure provided herein, one of ordinary skill in the art willrecognize a variety of equalizer circuits and/or architectures that maybe used in relation to different embodiments of the present invention.Where inter-track interference is not a concern (i.e., the tracks areseparated by substantial distance), continuous-time version of theequalized output 803 is represented by the following equation:r ₀ [t]=Σa ₀ [k]h ₀(t−kT),where a₀[k] represents the currently sensed bit period from the storagemedium, T denotes the duration of one bit, and h₀(t) represents theinter-symbol interference function (i.e., interference from adjacentsymbols along the same track). The inter-track interferencecorresponding to the two tracks on either side of the current track inequalized output 803 (i.e., an inter-track interference from a previoustrack r⁻¹(t), and an inter-track interference from a next track r₁(t))may be represented by the following equations, respectively:r ⁻¹(t)=Σa ⁻¹ [k]h ⁻¹(t−kT+τ ⁻¹)andr ₁(t)=Σa ₁ [k]h ₁(t−kT+τ ₁),where h⁻¹(t) represents the inter-track interference response from theprevious track, h₁(t) represents the inter-track interference responsefrom the next track, τ⁻¹ represents the phase delay of the track beingread with respect to the previous track, and τ₁ represents the phasedelay of the track being read with respect to the next track. Thefunctions h⁻¹(.) and h₁(.) are interference models based on variouscriteria including the relative proximity of adjacent tracks. Suchmodels may be developed for a particular storage device or medium.Accounting for the inter-track interference, equalized output 803 (incontinuous-time) may be represented by the following equation:r(t)=r ₀(t)+r ₁(t)+r ⁻¹(t).Thus, discrete-time version of the equalized output 803 may berepresented by the following equation:r[n]=r(nT)=Σa ₀ [k]g ₀ [n−k]+Σa ₁ [k]g ₁ [n−k]+Σa ⁻¹ [k]g ⁻¹ [n−k],where g₀[k]=h₀(kT), g₁[k]=h₁(kT+τ₁), and g⁻¹[k]=h⁻¹(kT+τ⁻¹).

Gap compensating inter-track interference compensation circuit 800includes a buffer 810 that stores hard data bits retrieved from aprevious track (i.e., a track located on a first side of the track beingprocessed) modified by hard bits corresponding to a track preceding theprevious track in the gaps of the previous track, and a buffer 815 thatstores hard data bits retrieved from a next track (i.e., a track locatedon a second side of the track being processed). These hard bits may bestored after a prior processing of data sensed from the respectivetracks (i.e., the previous track and the next track). The data frombuffer 810 is provided as a data output 812 and is denoted as a⁻¹[n],where n indicates the bit position within the track. The data frombuffer 815 is provided as a data output 814 and is denoted as a₁[n],where n indicates the bit position within the track. Data input 812 anddata input 814 are provided to an inter-track interference responseestimation circuit 820 and an inter-track interference estimator circuit825. In addition, equalized output 803 is provided to a latency circuit835.

Latency circuit 835 delays equalized output 803 in time to match thelatency involved in calculating inter-track interference responses byinter-track interference estimator circuit 820 and in calculatinginter-track interference by inter-track interference estimator circuit825. The delayed signals are provided as a delayed output 837 to aninter-track interference cancellation circuit 830.

Inter-track interference response estimator circuit 820 calculates anestimated inter-track interference response from the previous track(ĝ⁻¹[k]) and provides it as a previous track interference output 822.Previous track interference response 822 satisfies the followingequation:

${{\hat{g}}_{- 1}\lbrack k\rbrack} = {\frac{1}{N_{- 1}}{\sum\limits_{n = 1}^{N_{- 1}}{{a_{- 1}\left\lbrack {n - k} \right\rbrack} \cdot {{r\lbrack n\rbrack}.}}}}$where N⁻¹ is the number of data bits available from a previous track,and a⁻¹[n] are corresponding bits from a previous track. In some cases,the estimated outputs may be estimated using an adaptation approach,rather than by correlation computation. Similarly, the inter-trackinterference response circuit 820 provides an estimated inter-trackinterference response from the next track (ĝ₁[k]) that satisfies thefollowing equation:

${{{\hat{g}}_{1}\lbrack k\rbrack} = {\frac{1}{N_{1}}{\sum\limits_{n = 1}^{N_{1}}{{a_{1}\left\lbrack {n - k} \right\rbrack} \cdot {r\lbrack n\rbrack}}}}},$where N₁ is the number of data bits available from a next track, anda₁[n−k] are corresponding bits from a next track.

Next track interference response 824 and previous track interferenceresponse 822 are provided to inter-track interference estimator circuit825. Inter-track interference estimator circuit 825 estimates theinter-track interference from the previous track ({circumflex over(r)}⁻¹[n]) and provides it as a previous track interference output 827.Previous track interference output 827 is estimated (i.e., calculated)in accordance with the following equation:{circumflex over (r)} ⁻¹ [n]=Σa ⁻¹ [n−k]ĝ ⁻¹ [k].Similarly, inter-track interference estimator circuit 825 estimates theinter-track interference from the next track ({circumflex over (r)}₁[n])for the block m and provides it as a next track interference output 829.Next track interference output 829 is estimated (i.e., calculated) inaccordance with the following equation:{circumflex over (r)} ₁ [n]=Σa ₁ [n−k]ĝ ₁ [k].

Next track interference output 829 and previous track interferenceoutput 827 are provided to inter-track interference cancellation circuit830 along with delayed output 837. Inter-track interference cancellationcircuit 830 subtracts the inter-track interference signals from thedelayed output to yield an inter-track interference compensated output832 ({circumflex over (r)}₀[n]), across the bit periods included in theblock m. Inter-track interference compensated output 832 is calculatedin accordance with the following equation:{circumflex over (r)} ₀ [n]=r[n]−{circumflex over (r)} ₁ [n]−{circumflexover (r)} ⁻¹ [n].

A gap determination and hard data load circuit 890 receives hard data896 from the current track being processed, and loads it into previoustrack buffer 810. Such loading is prevented when hard data 896corresponds to a gap in the current track. The existence of a gap in thecurrent track is determined based on an end of sector 892 and a start ofsector 894. Thus, previous track buffer 810 is updated with hard datafrom the current track, except for when the current track has a gap inwhich case the data in previous track buffer 810 is not overwritten,leaving the data from the prior track. Thus, as the next track is readand processed, the data in previous track buffer 810 is the data fromthe previous track for regions where there is no gap, and data from thesecond previous track for gap regions of the previous track. As aspecific example using FIG. 2 b, where track N is being read andprocessed, the hard data corresponding to synchronization data 244, userdata region 246 and synchronization data 249 is written to previoustrack buffer 810 in preparation for later processing of track N+1. Incontrast, data previously written to previous track buffer 810 fromtrack N−1 that corresponds to gap 242 (i.e., a portion of user dataregion 250) and gap 248 (i.e., a portion of user data region 256) arenot overwritten and remain in previous track buffer 810 for use inrelation to cancelling inter-track interference for track N+1.

As just some of many advantages achievable through use of a gapcompensating inter-track interference cancellation circuit, inter-trackinterference can be compensated in a shingle writing situation whereinformation from multiple preceding tracks are accommodated in thecancellation. Based upon the disclosure provided herein, one of ordinaryskill in the art will recognize a variety of other advantages that maybe achieved in accordance with various embodiments of the presentinvention.

Turning to FIG. 9, a flow diagram 900 shows a shingled write approachthat may occur in relation to various embodiments of the presentinvention. Following flow diagram 900, an initial track to be written isselected (block 905). Using FIG. 2 b as an example, selecting theinitial track to be written may include selecting track N−2. Aread/write head assembly is positioned relative to the selected trackand it is determined whether the servo wedge data has been identified(block 910). Once the servo wedge data has been found and processed(block 910), user synchronization data preceding actual user data forthe sector is written between the servo wedge data regions (block 915).This synchronization data may be any synchronization data known in theart and is used to synchronize to the data during a read back. As thedata is a shingled write, the written data covers both the current trackbeing written and the next track. Thus, in the example, the data beingwritten covers the initially selected track N−2 and track N−1. Once thesynchronization data has been written (block 915), user data is written(block 920). Again, when the write is ongoing, the data is writtencovering the initially selected track N−2 and track N−1. Once the writeis completed (block 920), it is determined whether another sector is tobe written between the servo wedges (block 925). Where another sector isto be written (block 925), the processes of blocks 915-925 are repeatedfor the next sector. Otherwise, it is determined whether the track writeis complete (bock 930). Where the track is not complete (block 930), theprocesses of blocks 910-925 are repeated for the next servo wedge.Otherwise, the next track to be written is selected (block 905) and theprocesses of blocks 910-930 are repeated for the next track. Followingthe example of FIG. 2 b, the next track would be track N−1 which whenwritten would overwrite the spill over of the write to track N−2 ontotrack N−1, and the write to track N−1 will spill over onto track N.

Turning to FIG. 10, a flow diagram 1000 shows a method in accordancewith various embodiments of the present invention for gap compensationin an inter-track interference cancellation approach. Following flowdiagram 1000, a track to be read is selected (block 1005). Prior tomaking such a selection the hard data corresponding to the next trackand the previous track have been loaded into respective inter-trackinterference buffers. Thus, for example, where track N is selected forreading, a succeeding track inter-track interference buffer holding thehard data corresponding to the track N+1 is loaded, and the datacorresponding to track N−1 for the regions of user data region 250,synchronization data 254 and user data region 256, and the data fromtrack N−2 corresponding to gap 252 (i.e., a portion of gap 262 and asubsequent portion of synchronization data 264) and gap 258 (i.e., aportion of gap 268 and a subsequent portion of track N−2) is loaded intoa preceding track inter-track interference buffer.

A read/write head assembly is positioned relative to the selected trackand it is determined whether the servo wedge data has been identified(block 1010). Once the servo wedge data has been found and processed(block 1010), data is read from the selected track and stored as currentread data to a current read data buffer (bock 1015). Inter-trackinterference cancellation is performed on the current read data usingthe preceding track inter-track interference buffer and the succeedingtrack inter-track interference buffer to yield inter-track interferencecanceled data (block 1035). This inter-track interference canceled datais provided to a downstream data processing circuit to yield hard datacorresponding to the selected track (block 1040). Such downstreamprocessing may be any processing circuit known in the art. In oneparticular embodiment of the present invention, the downstreamprocessing may include performing one or more iterations of acombination of a maximum a posteriori data detection process and a lowdensity parity check decoding process. Based on the disclosure providedherein, one of ordinary skill in the art will recognize variousprocessing circuits and approaches that may be used in accordance withdifferent embodiments of the present invention to yield hard data fromthe inter-track interference canceled data.

As the hard data corresponding to the selected track become available itis determined whether the bits correspond to a gap in the current track(block 1045). Thus, using the example of FIG. 2 b, it is determinedwhether the hard data for the current track (e.g., track N) correspondsto gap 242 or gap 248. Where the hard data does not correspond to a gap(block 1045), the current read data is stored to the preceding trackinter-track interference buffer (block 1050). Otherwise, where the harddata correspond to a gap (block 1045), the prior value in the precedingtrack inter-track interference buffer remains as it is not overwrittenby the current data. Thus, using the example of FIG. 2 b where thecurrent track is track N, data from a portion of user data region 250 oftrack N−1 corresponding to gap 242 and data from a portion of user dataregion 256 of track N−1 corresponding to gap 248 remain in the precedingtrack inter-track interference buffer.

The next bit period is then selected (block 1055). It is determined ifthe end of the wedge (i.e., the region between servo data wedges) hasbeen reached (block 1060). Where the end of the wedge has not yet beenreached (block 1060), the processes of blocks 1015-1060 is repeated forthe next bit period. Alternatively, where the end of the wedge has beenreached (block 1060), it is determined whether the end of the track hasbeen reached (block 1065). Where the end of the track has not yet beenreached (block 1065), the processes of blocks 1010-1065 are repeated forthe remaining portion of the current track. Otherwise, the next track isselected and the processes of blocks 1010-1065 are repeated for the nexttrack. By following this approach, the preceding track inter-trackinterference buffer is prepared for processing the next track when aconsecutive track read is followed by including data from a trackpreceding the preceding track that corresponds to gaps in the precedingtrack.

Turning to FIG. 11, a combination gap compensating and frequency offsetcompensating inter-track interference cancellation circuit 1100 usdepicted in accordance with some embodiments of the present invention.Circuit 1100 receives an analog input signal 1177. Analog input signal1177 may be derived, for example, from a read/write head assembly (notshown) disposed in relation to a storage medium (not shown), andrepresents information sensed from the storage medium. Analog inputsignal 1177 is provided to an analog to digital converter circuit 1180that operates to convert the analog signal into a series of digitalsamples 1182 corresponding to analog input signal 1177. Analog todigital converter circuit 1180 may be any circuit known in the art thatis capable of converting an analog signal into corresponding series ofdigital samples. Based upon the disclosure provided herein, one ofordinary skill in the art will recognize a variety of analog to digitalconverter circuits and/or architectures that may be used in relation todifferent embodiments of the present invention. Digital samples 1182 areprovided to an equalizer circuit 1185 that equalizes the digital samplesand provides an equalized output 1103 (r[n]) to a block selector circuit1105. In some embodiments of the present invention, equalizer circuit1185 may be implemented as a digital finite impulse response circuit asare known in the art. Based upon the disclosure provided herein, one ofordinary skill in the art will recognize a variety of equalizer circuitsand/or architectures that may be used in relation to differentembodiments of the present invention. Where inter-track interference isnot a concern (i.e., the tracks are separated by substantial distance),continuous-time version of the equalized output 1103 is represented bythe following equation:r ₀ [t]=Σa ₀ [k]h ₀(t−kT),where a₀[k] represents the currently sensed bit period from the storagemedium, T denotes the duration of one bit, and h₀(t) represents theinter-symbol interference function (i.e., interference from adjacentsymbols along the same track). The inter-track interferencecorresponding to the two tracks on either side of the current track inequalized output 1103 (i.e., an inter-track interference from a previoustrack r⁻¹(t), and an inter-track interference from a next track r₁(t))may be represented by the following equations, respectively:r ⁻¹(t)=Σa ⁻¹ [k]h ⁻¹(t−kT+τ ⁻¹)andr ₁(t)=Σa ₁ [k]h ₁(t−kT+τ ₁),where h⁻¹(t) represents the inter-track interference response from theprevious track, h₁(t) represents the inter-track interference responsefrom the next track, τ⁻¹ represents the phase delay of the track beingread with respect to the previous track, and τ₁ represents the phasedelay of the track being read with respect to the next track. Thefunctions h⁻¹(.) and h₁(.) are interference models based on variouscriteria including the relative proximity of adjacent tracks. Suchmodels may be developed for a particular storage device or medium.Accounting for the inter-track interference, equalized output 1103 (incontinuous-time) may be represented by the following equation:r(t)=r ₀(t)+r ₁(t)+r ⁻¹(t).Thus, discrete-time version of the equalized output 1103 may berepresented by the following equation:r[n]=r(nT)=Σa ₀ [k]g ₀ [n−k]+Σa ₁ [k]g ₁ [n−k]+Σa ⁻¹ [k]g ⁻¹ [n−k],where g₀[k]=h₀(kT), g₁[k]=h₁(kT+τ₁), and g⁻¹[k]=h⁻¹(kT+τ⁻¹).

Combined gap compensating and frequency offset compensating inter-trackinterference compensation circuit 1100 includes a buffer 1110 thatstores hard data bits retrieved from a previous track (i.e., a tracklocated on a first side of the track being processed), and a buffer 1115that stores hard data bits retrieved from a next track (i.e., a tracklocated on a second side of the track being processed). These hard bitsmay be stored after a prior processing of data sensed from therespective tracks (i.e., the previous track and the next track). Thedata from buffer 1110 is provided as a data output 1112 and is denotedas a⁻¹[n], where n indicates the bit position within the track. The datafrom buffer 1115 is provided as a data output 1114 and is denoted asa₁[n], where n indicates the bit position within the track. Data input1112 and data input 1114 are provided to a block-wise estimation ofinter-track interference response circuit 1120 and an inter-trackinterference estimator circuit 1125.

A block selector circuit 1105 identifies a block 1107 of bit periods{r_(m)[n]} over which inter-track interference compensation is to beperformed, where m indicates the particular block that is selected and nindicates a given bit period along a track within the block. In somecases, the block size may be indicated as a letter i. In such cases, thevalue of n would extend from the first bit period in the selected blockto the first bit period plus i−1. Thus, for example, if the first bitperiod in the selected block is j, the block would include r[n], a₁[n]and a⁻¹[n] where n extends between j and i+j−1. The size of the blockselected may be predetermined and based upon a certain maximum frequencyerror and/or jitter expected between adjacent tracks, or may be variableand calculated based upon the estimated phase offset across a givennumber of sequential bit periods. Based upon the disclosure providedherein, one of ordinary skill in the art will recognize a variety ofblock sizes that may be used in relation to different embodiments of thepresent invention. Block 1107 is provided to block-wise estimation ofinter-track interference response circuit 1120, and to a block latencycircuit 1135.

Block latency circuit 1135 delays block 1107 in time to match thelatency involved in calculating inter-track interference responses byblock-wise estimation of inter-track interference response circuit 1120and in calculating inter-track interference by inter-track interferenceestimator circuit 1125. The delayed signals are provided as a delayedoutput 1137 to an inter-track interference cancellation circuit 1130.

A block-to-block shift estimation of inter-track interference responsecircuit 1140 calculates a phase delay 1142 of the track being read withrespect to the previous track, and a phase delay 1144 of the track beingread with respect to the next track. This calculation is done bydetermining the indices of the maximum tap coefficients in the estimatedinter-track interference responses that was used in generating previoustrack interference output 1127 and next track interference output 1129.Where the maximum filter tap of the inter-track interference responseused in calculating a respective one of previous track interferenceoutput 1127 is one of the taps to the right of center or the left ofcenter in block-wise estimation of inter-track interference responsecircuit 1120, then phase delay 1142 is selected to cause a shift of themaximum tap back toward the center of the filter. Similarly, where themaximum filter tap of the inter-track interference response used incalculating a respective one of next track interference output 1129 isone of the taps to the right of center or the left of center inblock-wise estimation of inter-track interference response circuit 1120,then phase delay 1144 is selected to cause a shift of the maximum tapback toward the center of the filter. Phase delay 1142 and phase delay1144 are provided along with data output 1112, data output 1114 andblock 1107 to block-wise estimation of inter-track interference responsecircuit 1120.

Block-wise estimation of inter-track interference response circuit 1120calculates an estimated inter-track interference response from theprevious track (ĝ_(−1,m)[k]) and provides it as a previous trackinterference output 1122. Previous track interference response 1122satisfies the following equation:

${{\hat{g}}_{{- 1},m}\lbrack k\rbrack} = {\frac{1}{N_{- 1}}{\sum\limits_{n = 1}^{N_{- 1}}{{a_{- 1}\left\lbrack {n + {\left( {m - 1} \right)N_{b}} - k - \delta_{{- 1},m}} \right\rbrack} \cdot {r\left\lbrack {n + {\left( {m - 1} \right)N_{b}}} \right\rbrack}}}}$     δ_(−1, m) = δ_(−1, m − 1) + k_(−1, m − 1)where δ_(−1,m) denotes the shift in correlator reference required forcentering the inter-track interference response from the previous trackĝ_(−1,m)[k], N_(b) denotes the block-size, and k_(−1,m−1) denotes indexof the maximum tap coefficient in ĝ_(−1,m−1)[k]. In some cases, theestimated outputs may be estimated using an adaptive approach, ratherthan by correlation computation. Similarly, block-wise estimation ofinter-track interference response circuit 1120 calculates an estimatedinter-track interference response from the next track (ĝ_(1,m)[k]) andprovides it as a next track interference response 1124. Next trackinterference response 1124 is calculated in accordance with thefollowing equation:

${{\hat{g}}_{1,m}\lbrack k\rbrack} = {\frac{1}{N_{1}}{\sum\limits_{n = 1}^{N_{- 1}}{{a_{1}\left\lbrack {n + {\left( {m - 1} \right)N_{b}} - k - \delta_{1,m}} \right\rbrack} \cdot {r\left\lbrack {n + {\left( {m - 1} \right)N_{b}}} \right\rbrack}}}}$     δ_(1, m) = δ_(1, m − 1) + k_(1, m − 1)where δ_(1,m) denotes the shift in correlator reference required forcentering the inter-track interference response from the previous trackĝ_(1,m)[k] and k_(1,m−1) denotes index of the maximum tap coefficient inĝ_(1,m−1)[k]. Starting phase offsets δ_(−1,0) and δ_(1,0) areinitialized to zero, if sectors are phase synchronized at the beginningand/or if no a priori information on phase offset is available.

Next track interference response 1124 and previous track interferenceresponse 1122 are provided to inter-track interference estimator circuit1125. Inter-track interference estimator circuit 1125 estimates theinter-track interference from the previous track ({{circumflex over(r)}_(−1,m)[n]}) for the block m and provides it as a previous trackinterference output 1127. Previous track interference output 1127 isestimated (i.e., calculated) in accordance with the following equation:{circumflex over (r)} _(−1,m) [n]=Σa ⁻¹ [n+(m−1)N _(b)−δ_(−1,m) −k]ĝ_(−1,m) [k],across the bit periods included in the block m. Similarly, inter-trackinterference estimator circuit 325 estimates the inter-trackinterference from the next track ({{circumflex over (r)}_(1,m)[n]}) forthe block m and provides it as a next track interference output 1129.Next track interference output 1129 is estimated (i.e., calculated) inaccordance with the following equation:{circumflex over (r)} _(1,m) [n]=Σa ₁ [n+(m−1)N _(b)−δ_(1,m) −k]ĝ _(1,m)[k],across the bit periods included in the block m.

Next track interference output 1129 and previous track interferenceoutput 1127 are provided to inter-track interference cancellationcircuit 1130 along with delayed output 1137. Inter-track interferencecancellation circuit 1130 subtracts the inter-track interference signalsfrom the delayed output to yield an inter-track interference compensatedoutput 1132 ({{circumflex over (r)}_(0,m)[n]}), across the bit periodsincluded in the block m. Inter-track interference compensated output1132 is calculated in accordance with the following equation:{circumflex over (r)} _(0,m) [n]=r _(m) [n]−{circumflex over (r)} _(1,m)[n]−{circumflex over (r)} _(−1,m) [n],across the bit periods included in the block m.

A gap determination and hard data load circuit 1190 receives hard data1196 from the current track being processed, and loads it into previoustrack buffer 1110. Such loading is prevented when hard data 1196corresponds to a gap in the current track. The existence of a gap in thecurrent track is determined based on an end of sector 1192 and a startof sector 1194. Thus, previous track buffer 1110 is updated with harddata from the current track, except for when the current track has a gapin which case the data in previous track buffer 1110 is not overwritten,leaving the data from the prior track. Thus, as the next track is readand processed, the data in previous track buffer 1110 is the data fromthe previous track for regions where there is no gap, and data from thesecond previous track for gap regions of the previous track. As aspecific example using FIG. 2 b, where track N is being read andprocessed, the hard data corresponding to synchronization data 244, userdata region 246 and synchronization data 249 is written to previoustrack buffer 1110 in preparation for later processing of track N+1. Incontrast, data previously written to previous track buffer 1110 fromtrack N−1 that corresponds to gap 242 (i.e., a portion of user dataregion 250) and gap 248 (i.e., a portion of user data region 256) arenot overwritten and remain in previous track buffer 1110 for use inrelation to cancelling inter-track interference for track N+1.

As just some of many advantages achievable through use of gapcompensating and frequency offset compensating a block-wise inter-trackinterference estimation and cancellation circuitry: inter-trackinterference can be compensated using less circuitry than may berequired if a digital phase locked loop and interpolation techniques areused to compensate; and inter-track interference can be compensated in ashingled writing situation where information from multiple precedingtracks are accommodated in the cancellation. Based upon the disclosureprovided herein, one of ordinary skill in the art will recognize avariety of other advantages that may be achieved in accordance withvarious embodiments of the present invention.

Turning to FIG. 12, a flow diagram 1200 shows a method in accordancewith some embodiments of the present invention for block-wise gapcompensation and frequency offset compensation in an inter-trackinterference cancellation approach. Following flow diagram 1200, a trackto be read is selected (block 1205). Prior to making such a selectionthe hard data corresponding to the next track and the previous trackhave been loaded into respective inter-track interference buffers. Thus,for example, where track N is selected for reading, a succeeding trackinter-track interference buffer holding the hard data corresponding tothe track N+1 is loaded, and the data corresponding to track N−1 for theregions of user data region 250, synchronization data 254 and user dataregion 256, and the data from track N−2 corresponding to gap 252 (i.e.,a portion of gap 262 and a subsequent portion of synchronization data264) and gap 258 (i.e., a portion of gap 268 and a subsequent portion oftrack N−2) is loaded into a preceding track inter-track interferencebuffer.

In addition, the size of the blocks to be treated together duringblock-wise inter-track interference compensation is selected (block1207). The size of the blocks selected may be predetermined and basedupon a certain maximum frequency error and/or jitter expected betweenadjacent tracks, or may be variable and calculated based upon theestimated phase offset across a given number of sequential bit periods.Based upon the disclosure provided herein, one of ordinary skill in theart will recognize a variety of block sizes that may be used in relationto different embodiments of the present invention.

A read/write head assembly is positioned relative to the selected trackand it is determined whether the servo wedge data has been identified(block 1210). Once the servo wedge data has been found and processed(block 1210), block processing for the current block begins (block1213). Data is read from the selected track and stored as current readdata to a current read data buffer (bock 1215). Inter-track interferencecancellation is performed on the current read data using the precedingtrack inter-track interference buffer and the succeeding trackinter-track interference buffer to yield inter-track interferencecanceled data (block 1235). This inter-track interference canceled datais provided to a downstream data processing circuit to yield hard datacorresponding to the selected track (block 1240). Such downstreamprocessing may be any processing circuit known in the art. In oneparticular embodiment of the present invention, the downstreamprocessing may include performing one or more iterations of acombination of a maximum a posteriori data detection process and a lowdensity parity check decoding process. Based on the disclosure providedherein, one of ordinary skill in the art will recognize variousprocessing circuits and approaches that may be used in accordance withdifferent embodiments of the present invention to yield hard data fromthe inter-track interference canceled data.

As the hard data corresponding to the selected track become available itis determined whether the bits correspond to a gap in the current track(block 1245). Thus, using the example of FIG. 2 b, it is determinedwhether the hard data for the current track (e.g., track N) correspondsto gap 242 or gap 248. Where the hard data does not correspond to a gap(block 1245), the current read data is stored to the preceding trackinter-track interference buffer (block 1250). Otherwise, where the harddata correspond to a gap (block 1245), the prior value in the precedingtrack inter-track interference buffer remains as it is not overwrittenby the current data. Thus, using the example of FIG. 2 b where thecurrent track is track N, data from a portion of user data region 250 oftrack N−1 corresponding to gap 242 and data from a portion of user dataregion 256 of track N−1 corresponding to gap 248 remain in the precedingtrack inter-track interference buffer.

The next bit period is then selected (block 1255). It is then determinedwhether the next bit period is within the currently processing block, oris beyond the currently processing block (block 1257). Where the nextbit period is within the currently processing block (block 1257), theprocesses of blocks 1215-1257 is repeated for the next bit period.Otherwise, where the next bit period is outside the currently processingblock (block 1257), it is determined if the end of the wedge (i.e., theregion between servo data wedges) has been reached (block 1260). Wherethe end of the wedge has not yet been reached (block 1260), theprocesses of blocks 1213-1260 is repeated for the next block.Alternatively, where the end of the wedge has been reached (block 1260),it is determined whether the end of the track has been reached (block1265). Where the end of the track has not yet been reached (block 1265),the processes of blocks 1210-1265 are repeated for the remaining portionof the current track. Otherwise, the next track is selected and theprocesses of blocks 1210-1265 are repeated for the next track. Byfollowing this approach, the preceding track inter-track interferencebuffer is prepared for processing the next track when a consecutivetrack read is followed by including data from a track preceding thepreceding track that corresponds to gaps in the preceding track.

FIG. 13 depicts a data alignment based inter-track interferencecancellation circuit 1300 in accordance with some embodiments of thepresent invention. Inter-track interference compensation circuit 1300receives an analog input signal 1377. Analog input signal 1377 may bederived, for example, from a read/write head assembly (not shown)disposed in relation to a storage medium (not shown), and representsinformation sensed from the storage medium. Analog input signal 1377 isprovided to an analog to digital converter circuit 1380 that operates toconvert the analog signal into a series of digital samples 1382corresponding to analog input signal 1377. Analog to digital convertercircuit 1380 may be any circuit known in the art that is capable ofconverting an analog signal into corresponding series of digitalsamples. Based upon the disclosure provided herein, one of ordinaryskill in the art will recognize a variety of analog to digital convertercircuits and/or architectures that may be used in relation to differentembodiments of the present invention. Digital samples 1382 are providedto an equalizer circuit 1385 that equalizes the digital samples andprovides an equalized output 1303 (r[n]) to a correlation basedinter-track interference response estimation circuit 1320. In someembodiments of the present invention, equalizer circuit 1385 may beimplemented as a digital finite impulse response circuit as are known inthe art. Based upon the disclosure provided herein, one of ordinaryskill in the art will recognize a variety of equalizer circuits and/orarchitectures that may be used in relation to different embodiments ofthe present invention. Where inter-track interference is not a concern(i.e., the tracks are separated by substantial distance),continuous-time version of the equalized output 1303 is represented bythe following equation:r ₀ [t]=Σa ₀ [k]h ₀(t−kT),where a₀[k] represents the currently sensed bit period from the storagemedium, T denotes the duration of one bit, and h₀(t) represents theinter-symbol interference function (i.e., interference from adjacentsymbols along the same track). The inter-track interferencecorresponding to the two tracks on either side of the current track inequalized output 1303 (i.e., an inter-track interference from a previoustrack r⁻¹(t), and an inter-track interference from a next track r₁(t))may be represented by the following equations, respectively:r ⁻¹(t)=Σa ⁻¹ [k]h ⁻¹(t−kT+τ ⁻¹)andr ₁(t)=Σa ₁ [k]h ₁(t−kT+τ ₁),where h⁻¹(t) represents the inter-track interference response from theprevious track, h₁(t) represents the inter-track interference responsefrom the next track, τ⁻¹ represents the phase delay of the track beingread with respect to the previous track, and τ₁ represents the phasedelay of the track being read with respect to the next track. Thefunctions h⁻¹(.) and h₁(.) are interference models based on variouscriteria including the relative proximity of adjacent tracks. Suchmodels may be developed for a particular storage device or medium.Accounting for the inter-track interference, equalized output 1303 (incontinuous-time) may be represented by the following equation:r(t)=r ₀(t)+r ₁(t)+r ⁻¹(t).Thus, discrete-time version of the equalized output 1303 may berepresented by the following equation:r[n]=r(nT)=Σa ₀ [k]g ₀ [n−k]+Σa ₁ [k]g ₁ [n−k]+Σa ⁻¹ [k]g ⁻¹ [n−k],where g₀[k]=h₀(kT), g₁[k]=h₁(kT+τ₁), and g⁻¹[k]=h⁻¹(kT+τ⁻¹). Assuming{a₀[n], a⁻¹[n], a₁[n]} are mutually uncorrelated bit streams, theexpected values for the functions h⁻¹ (.) and h₁(.) are defined asfollows:E[r[n]·a ⁻¹ [n−n ⁻¹ ]]=g ⁻¹ [n ⁻¹ ]=h ⁻¹(n ⁻¹ T+{circumflex over (τ)}⁻¹);andE[r[n]·a ₁ [n−n ₁ ]]=g ⁻¹ [n ₁ ]=h ₁(n ₁ T+{circumflex over (τ)} ₁),respectively.

Inter-track interference compensation circuit 1300 includes a buffer1310 that stores hard data bits retrieved from a previous track (i.e., atrack located on a first side of the track being processed), and abuffer 1315 that stores hard data bits retrieved from a next track(i.e., a track located on a second side of the track being processed).These hard bits may be stored after a prior processing of data sensedfrom the respective tracks (i.e., the previous track and the nexttrack). The data from buffer 1310 is provided as a data output 1312 andis denoted as a⁻¹[n], where n indicates the bit position within thetrack. The data from buffer 1315 is provided as a data output 1314 andis denoted as a₁[n], where n indicates the bit position within thetrack. Data input 1312 and data input 1314 are provided to correlationbased inter-track interference response circuit 1320 and an inter-trackinterference estimator circuit 1325.

Latency circuit 1335 delays equalized output 1303 in time to match thelatency involved in calculating inter-track interference responses byinter-track interference estimator circuit 1320 and in calculatinginter-track interference by inter-track interference estimator circuit1325. The delayed signals are provided as a delayed output 1337 to aninter-track interference cancellation circuit 1330. The equalized output1303 is also given as inputs to previous and next track sync markreflection detector circuit 1350, and previous and next track phasealignment pre-processor circuit 1370.

Correlation based inter-track interference response circuit 1320calculates an estimated inter-track interference response from theprevious track (ĝ⁻¹[k]) and provides it as a previous track interferenceoutput 1322. Previous track interference response 1322 satisfies thefollowing equation:

${{{\hat{g}}_{- 1}\lbrack k\rbrack} = {\frac{1}{N_{- 1}}{\sum\limits_{n = 1}^{N_{- 1}}{{a_{- 1}\left\lbrack {n - k} \right\rbrack} \cdot {r\lbrack n\rbrack}}}}},$where N⁻¹ is the number of data bits available from a previous track,and a⁻¹[n] are corresponding bits from a previous track. Similarly,correlation based inter-track interference response circuit 1320provides an estimated inter-track interference response from the nexttrack (ĝ₁[k]) that satisfies the following equation:

${{{\hat{g}}_{1}\lbrack k\rbrack} = {\frac{1}{N_{1}}{\sum\limits_{n = 1}^{N_{1}}{{a_{1}\left\lbrack {n - k} \right\rbrack} \cdot {r\lbrack n\rbrack}}}}},$where N₁ is the number of data bits available from a next track, anda₁[n] are corresponding bits from a next track.

Next track interference response 1324 and previous track interferenceresponse 1322 are provided to inter-track interference estimator circuit1325. Inter-track interference estimator circuit 1325 estimates theinter-track interference from the previous track ({{circumflex over(r)}⁻¹[n]}) for the track and provides it as a previous trackinterference output 1327. Previous track interference output 1327 isestimated (i.e., calculated) in accordance with the following equation:{circumflex over (r)} ⁻¹ [n]=Σa ⁻¹ [n−k]ĝ ⁻¹ [k],across the bit periods for the track. Similarly, inter-trackinterference estimator circuit 1325 estimates the inter-trackinterference from the next track ({{circumflex over (r)}₁[n]}) for thebit periods and provides it as a next track interference output 1329.Next track interference output 1329 is estimated (i.e., calculated) inaccordance with the following equation:{circumflex over (r)} ₁ [n]=Σa ₁ [n−k]ĝ ₁ [k],across the bit periods included in the track.

Next track interference output 1329 and previous track interferenceoutput 1327 are provided to inter-track interference cancellationcircuit 1330. Inter-track interference cancellation circuit 1330subtracts the inter-track interference signals from the delayed outputto yield an inter-track interference compensated output 1332({{circumflex over (r)}₀[n]}), across the bit periods included in thetrack. Inter-track interference compensated output 1332 is calculated inaccordance with the following equation:{circumflex over (r)} ₀ [n]=r[n]−{circumflex over (r)} ₁ [n]−{circumflexover (r)} ⁻¹ [n],across the bit periods included in the track.

Equalized output 1303, data output 1312 from previous track buffer 1310and data output 1314 from next track buffer 1315 are also provided to aprevious track and next track sync mark reflection detector circuit1350. Previous track and next track sync mark reflection detectorcircuit 1350 queries the equalized output 1303 for reflection of syncmarks from previous track and next track through inter-trackinterference. When the sync mark of the previous track is identified inequalized output 1303, a previous sync found signal 1352 is asserted. Itshould be noted that in some cases only the pattern corresponding to theprevious track sync mark is queried in making a determination as towhether to assert previous sync found signal 1352. In other cases whereadditional robustness is desired, a combination of the patterncorresponding to the previous track sync mark and at least a portion ofa preceding preamble pattern is queried in making a determination as towhether to assert previous sync found signal 1352. Similarly, when thesync mark of the next track is identified in equalized output 1303, anext sync found signal 1353 is asserted. It should be noted that in somecases only the pattern corresponding to the next track sync mark isqueried in making a determination as to whether to assert next syncfound signal 1353. In other cases where additional robustness isdesired, a combination of the pattern corresponding to the next tracksync mark and at least a portion of a preceding preamble pattern isqueried in making a determination as to whether to assert next syncfound signal 1353. As discussed below in relation to FIG. 14, the syncmarks in the previous track, next track and current track are carefullyselected to be as mutually dissimilar (orthogonal) to avoid confusionbetween the tracks. Based upon the disclosure provided herein, one ofordinary skill in the art will recognize a variety of methods and/orarchitectures to locate sync marks from current track, previous trackand next track in the equalized output 1303 that may be used in relationto different embodiments of the present invention.

Turning to FIG. 14, an example track to track layout 1400 exhibitingsubstantial track to track offsets shows a situation where threedistinct sync marks are used across adjacent tracks. In particular,track layout 1400 includes: a track 1405 that includes a 2 T preamblefollowing by a first sync data (sync data 1); a track 1410 that includesa 2 T preamble followed by a second sync data (sync data 2); a track1415 that includes a 2 T preamble followed by a third sync data (syncdata 3); a track 1420 that includes a 2 T preamble following by a firstsync data (sync data 1); a track 1425 that includes a 2 T preamblefollowed by a second sync data (sync data 2); a track 1430 that includesa 2 T preamble followed by a third sync data (sync data 3); and a track1435 that includes a 2 T preamble following by a first sync data (syncdata 1). Of note, many more than the seven depicted tracks may beincluded.

None of the three sync marks (sync data 1, sync data 2 and sync data 3)is adjacent to a track utilizing the same sync mark, and the sync marksare selected such that they are maximally separate from each other interms of correlation. This allows for detecting a reflection (i.e.,inter-track interference from a given sync mark in the adjacent track.In the case where the data is misaligned like that shown in track layout1400, the sync mark from one track is reflected at a non-sync marklocation in an adjacent track. In particular, sync data 1 from track1405 is reflected in both sync data 2 and bit 2,1 of track 1410; syncdata 2 from track 1410 is reflected in both 2 T preamble and sync data 1of track 1405, and in both sync data 3 and bit 3,1 of track 1415; syncdata 3 from track 1415 is reflected in both 2 T preamble and sync data 2of track 1410, and in both 2 T preamble and sync data 1 of track 1420;sync data 1 from track 1420 is reflected in both sync data 3 and bit 3,1of track 1415, and in both 2 T preamble and sync data 2 of track 1425;sync data 2 from track 1425 is reflected in both sync data 1 and bit 4,1of track 1420, and in sync data 3, bit 6,1 and bit 6,2 of track 1430;and sync data 3 from track 1430 is reflected in both 2 T preamble andsync data 2 of track 1425, and in both 2 T preamble and sync data 1 oftrack 1435.

Referring again to FIG. 13, the equalized output 1303 is also providedto a current track sync mark detector circuit 1355. Current track syncmark detector circuit 1355 queries the equalized output 1303 for a syncmark included in the data stream. When the sync mark of the currenttrack is identified in equalized output 1303, a current sync foundsignal 1357 is asserted. It should be noted that in some cases only thepattern corresponding to the current track sync mark is queried inmaking a determination as to whether to assert current sync found signal1357. In other cases where additional robustness is desired, acombination of the pattern corresponding to the current track sync markand at least a portion of a preceding preamble pattern is queried inmaking a determination as to whether to assert current sync found signal1357. In another embodiment of the present invention, the sync markdetection is done using inter-track interference compensated output 1332in place of equalized output 1303.

Current sync found signal 1357, next sync found signal 1353 and previoussync found signal 1352 are provided to a phase difference calculatorcircuit 1360. Phase difference calculator circuit calculates offset 1362between previous sync found signal 1352 and the current sync foundsignal 1357, and offset 1363 between next sync found signal 1353 and thecurrent sync found signal 1357, and provides these offsets as inputs tointer-track interference response estimation circuit 1320 andinter-track interference estimator circuit 1325. Inter-trackinterference response estimation circuit 1320 and inter-trackinterference estimator circuit 1325 use the received offsets informationto align data output 1312 (i.e., a⁻¹[n]) from previous track buffer 1310and data output 1314 from next track buffer 1315 with equalized output1303 (i.e., r[n]).

In another embodiment of the current invention, the previous track andnext track sync mark reflection detector circuit 1350 is replaced with aprevious track and next track phase alignment pre-processor 1370.Equalized output 1303, data output 1312 from previous track buffer 1310,data output 1314 from next track buffer 1315 and current track syncfound signal 1357 from current track sync mark detector circuit 1355 areprovided as inputs to the phase alignment pre-processor 1370. Theprevious track and next track phase alignment pre-processor estimatesinter-track interference responses of very long lengths for previoustrack and next track. The location of the maximum coefficient in theestimated inter-track interference responses from previous track andnext track are output as initial phase estimate for previous track 1372and initial phase estimate for next track 1373. The estimated initialphases 1372 and 1373 are provided as inputs to inter-track responseestimator circuit 1320 and inter-track signal estimator circuit 1325 toappropriately align the data output 1312 from previous track buffer 1310and data output 1314 from next track buffer 1315 with the equalizedoutput 1303. Estimation of inter-track interference responses for phaseestimation is performed using the same algorithm described above inconnection with FIG. 14 over a short block of samples (e.g., 3000) fromthe beginning of the sector. Based upon the disclosure provided herein,one of ordinary skill in the art will recognize a variety of methodsand/or architectures that may be used in relation to differentembodiments of the present invention to locate the phase offsets of datawritten on previous track and next track with that on current track. Itis also worthy of mention that the phase offset estimation performed byphase alignment pre-processor 1370 and sync mark reflection detectorcircuit 1350 in conjunction with phase difference calculator circuit1360 are operating to make the mis-aligned sector format in FIG. 2 beffectively look like the aligned sector format in FIG. 2 c.

It should be noted that the approach discussed in relation tointer-track interference compensation circuit 1300 estimates phaseoffsets of previous track and next track with current track and cancelsinter-track interference from both a previous and a next track. Theapproach may be simplified to cancel inter-track interference from onlyone of the previous track or the next track, with alignment only withthe sync mark from the corresponding track being completed.

Turning to FIG. 15, a flow diagram 1500 shows a method in accordancewith some embodiments of the present invention for offset compensationin an inter-track interference cancellation approach. Following flowdiagram 1500, a track to be read is selected (block 1505). Prior tomaking such a selection the hard data corresponding to the next trackand the previous track have been loaded into respective inter-trackinterference buffers. Thus, using track layout 1400 as an example, wheretrack 1420 is selected for reading, a preceding track inter-trackinterference buffer holding the hard data corresponding to track 1415 isloaded, and the data corresponding to track 1425 was previously loadedinto a next track inter-track interference buffer.

A read/write head assembly is positioned relative to the selected trackand it is determined whether the servo wedge data has been identified(block 1510). Once the servo wedge data has been found and processed(block 1510), data is read from the selected track and stored as currentread data to a current read data buffer (bock 1515). In addition, theread data from the current track is queried to determine whether thesync mark from the previous track is included (block 1525). In somecases, more than just the pattern corresponding to the previous tracksync mark is queried. For example, a combination of the patterncorresponding to the previous track sync mark and at least a portion ofa preceding preamble pattern is queried. Similarly, the read data fromthe current track is queried to determine whether the sync mark from thenext track is included (block 1540). Again, in some cases, more thanjust the pattern corresponding to the next track sync mark is queried.In addition, the read data from current track is queried to determinewhether the sync mark from the current track is included (block 1545).Again, in some cases, more than just the pattern corresponding to thecurrent track sync mark is queried.

Where the sync mark from the previous track is identified (block 1530),the sync mark from the next track is identified (block 1540) and thecurrent sync mark is identified (block 1545), a first offset between theprevious track and the current track is calculated and a second offsetbetween the next track and the current track is calculated (block 1550).These offsets are then used to align the data from the previous trackinter-track interference buffer and the data from the next trackinter-track interference buffer with the current data (bock 1555). Theinter-track interference from the previous track ({{circumflex over(r)}⁻¹[n]}) is calculated (block 1520), and the inter-track interferencefrom the next track ({{circumflex over (r)}₁[n]}) is calculated (block1525). The inter-track interference from the next track and theinter-track interference from the previous track are subtracted from thecurrently read data to yield the inter-track interference canceled data({{circumflex over (r)}₀[n]}) (block 1535). In addition, the currentdata is stored to the previous track inter-track interference buffer(block 1560), and the next bit period is selected for reading (block1565).

Alternatively, where the sync marks for the previous track, the nexttrack and the current track are not yet found (block 1530, block 1540,block 1545), the current data is stored to the previous trackinter-track interference buffer (block 1560), and the next bit period isselected for reading (block 1565). It is determined if the end of thewedge (i.e., the region between servo data wedges) has been reached(block 1570). Where the end of the wedge has not yet been reached (block1570), the processes of blocks 1515-1565 is repeated for the next block.Alternatively, where the end of the wedge has been reached (block 1570),it is determined whether the end of the track has been reached (block1575). Where the end of the track has not yet been reached (block 1575),the processes of blocks 1510-1565 are repeated for the remaining portionof the current track. Otherwise, the next track is selected and theprocesses of blocks 1510-1565 are repeated for the next track.

Turning to FIG. 16, a storage system 1600 is shown including a readchannel circuit 1610 with an inter-track interference compensationcircuit in accordance with various embodiments of the present invention.Storage system 1600 may be, for example, a hard disk drive. Storagesystem 1600 also includes a preamplifier 1670, an interface controller1620, a hard disk controller 1666, a motor controller 1668, a spindlemotor 1672, a disk platter 1678, and a read/write head 1676. Interfacecontroller 1620 controls addressing and timing of data to/from diskplatter 1678. The data on disk platter 1678 consists of groups ofmagnetic signals that may be detected by read/write head assembly 1676when the assembly is properly positioned over disk platter 1678. In oneembodiment, disk platter 1678 includes magnetic signals recorded inaccordance with either a longitudinal or a perpendicular recordingscheme.

In a typical read operation, read/write head assembly 1676 is accuratelypositioned by motor controller 1668 over a desired data track on diskplatter 1678. Motor controller 1668 both positions read/write headassembly 1676 in relation to disk platter 1678 and drives spindle motor1672 by moving read/write head assembly to the proper data track on diskplatter 1678 under the direction of hard disk controller 1666. Spindlemotor 1672 spins disk platter 1678 at a determined spin rate (RPMs).Once read/write head assembly 1678 is positioned adjacent the properdata track, magnetic signals representing data on disk platter 1678 aresensed by read/write head assembly 1676 as disk platter 1678 is rotatedby spindle motor 1672. The sensed magnetic signals are provided as acontinuous, minute analog signal representative of the magnetic data ondisk platter 1678. This minute analog signal is transferred fromread/write head assembly 1676 to read channel 1610 via preamplifier1670. Preamplifier 1670 is operable to amplify the minute analog signalsaccessed from disk platter 1678. In turn, read channel circuit 1610decodes and digitizes the received analog signal to recreate theinformation originally written to disk platter 1678. This data isprovided as read data 1603 to a receiving circuit. As part of processingthe received information, read channel circuit 1610 performs aninter-track interference compensation. Such an inter-track interferencecompensation circuit may be implemented similar to that described abovein relation to FIG. 3, FIG. 5, FIG. 7, FIG. 8, FIG. 11 and/or FIG. 13,and/or may operate similar to the method discussed in relation to FIG.4, FIG. 6, FIG. 9, FIG. 10, FIG. 12, and/or FIG. 15. A write operationis substantially the opposite of the preceding read operation with writedata 1601 being provided to read channel circuit 1610. This data is thenencoded and written to disk platter 1678.

It should be noted that storage system 1600 may be integrated into alarger storage system such as, for example, a RAID (redundant array ofinexpensive disks or redundant array of independent disks) based storagesystem. It should also be noted that various functions or blocks ofstorage system 1600 may be implemented in either software or firmware,while other functions or blocks are implemented in hardware.

It should be noted that the various blocks discussed in the aboveapplication may be implemented in integrated circuits along with otherfunctionality. Such integrated circuits may include all of the functionsof a given block, system or circuit, or only a subset of the block,system or circuit. Further, elements of the blocks, systems or circuitsmay be implemented across multiple integrated circuits. Such integratedcircuits may be any type of integrated circuit known in the artincluding, but are not limited to, a monolithic integrated circuit, aflip chip integrated circuit, a multichip module integrated circuit,and/or a mixed signal integrated circuit. It should also be noted thatvarious functions of the blocks, systems or circuits discussed hereinmay be implemented in either software or firmware. In some such cases,the entire system, block or circuit may be implemented using itssoftware or firmware equivalent. In other cases, the one part of a givensystem, block or circuit may be implemented in software or firmware,while other parts are implemented in hardware.

In conclusion, the invention provides novel systems, devices, methodsand arrangements for processing data from a storage medium. Whiledetailed descriptions of one or more embodiments of the invention havebeen given above, various alternatives, modifications, and equivalentswill be apparent to those skilled in the art without varying from thespirit of the invention. For example, one or more embodiments of thepresent invention may be applied to various data storage systems anddigital communication systems, such as, for example, tape recordingsystems, optical disk drives, wireless systems, and digital subscriberline systems. Therefore, the above description should not be taken aslimiting the scope of the invention, which is defined by the appendedclaims.

What is claimed is:
 1. A non-zero gap, inter-track interferencecompensation circuit, the compensation circuit comprising: aninter-track interference determination circuit operable to calculate aninter-track interference from a previous track data set based at leastin part on the previous track data set and a current track data set,wherein the previous track data set includes a gap, wherein a portion ofthe data in the previous track data set corresponds to a previous trackon a storage medium, and wherein the data in the previous track data setcorresponding to the gap corresponds to a track preceding a previoustrack.
 2. The circuit of claim 1, wherein the circuit further comprises:a data buffer operable to store the previous track data set; and a harddata load circuit operable determine a location of the gap and to loadthe previous track data set into the data buffer.
 3. The circuit ofclaim 2, wherein the gap is an unused area between a sync mark regionand a user data region.
 4. The circuit of claim 3, wherein at least aportion of the user data region is written with data corresponding tothe track preceding the previous track, and is overwritten with datacorresponding to the previous track.
 5. The circuit of claim 3, whereinat least a portion of the sync mark region is written with datacorresponding to the track preceding the previous track, and isoverwritten with data corresponding to the previous track.
 6. Thecircuit of claim 3, wherein at least a portion of the gap is writtenwith data corresponding to the track preceding the previous track, andis not overwritten with data corresponding to the previous track.
 7. Thecircuit of claim 2, wherein the gap is written with data correspondingto the track preceding the previous track.
 8. The circuit of claim 2,wherein the inter-track interference determination circuit comprises: aninter-track interference response circuit operable to estimate aninter-track interference response from the previous track data set basedat least in part on the previous track data set and a current track dataset; and an inter-track interference signal estimator circuit operableto calculate an inter-track interference from the previous track dataset based at least in part on the previous track data set and theinter-track interference response from the previous track data set. 9.The circuit of claim 1, wherein the circuit is implemented as part of anintegrated circuit.
 10. The circuit of claim 1, wherein the circuit isdeployed as part of a hard disk drive.
 11. The circuit of claim 1,wherein the circuit further comprises: an inter-track interferencecancellation circuit operable to cancel the inter-track interferencefrom the previous track data set to yield a compensated output.
 12. Amethod for cancelling inter-track interference in a non-zero gap dataset, the method comprising: receiving a current track data set derivedfrom a current track on a storage medium; accessing a previous trackdata set, wherein the previous track data set was at least in partderived from a previous track on the storage medium, and wherein theprevious track data set includes a gap having data that corresponds to atrack preceding the previous track on the storage medium calculating anestimated inter-track interference response from the previous track dataset based at least in part on the current track data set and theprevious track data set; and calculating an inter-track interferencefrom the previous track data set based at least in part on the previoustrack data set and the inter-track interference response from theprevious track data set.
 13. The method of claim 12, wherein the methodfurther comprises: cancelling the inter-track interference from theprevious track data set to yield a compensated output.
 14. The method ofclaim 12, wherein the gap is an unused area between a sync mark regionand a user data region.
 15. The method of claim 14, wherein at least aportion of the user data region and at least a portion of the sync markregion are written with data corresponding to the track preceding theprevious track, and are overwritten with data corresponding to theprevious track.
 16. The method of claim 14, wherein at least a portionof the gap is written with data corresponding to the track preceding theprevious track, and is not overwritten with data corresponding to theprevious track.
 17. The method of claim 12, wherein the gap is writtenwith data corresponding to the track preceding the previous track.
 18. Adata storage device, the data storage device comprising: a storagemedium; a read/write head assembly disposed in relation to the storagemedium; a read channel circuit operable to receive an information setfrom the storage medium via the read/write head assembly, the readchannel circuit including: a front end circuit operable to convert theinformation set to a current track data set; a data buffer; a hard dataload circuit operable determine a location of a gap in a data setderived from a previous track and to load a previous track data set intothe data buffer, wherein the previous track data set includes datacorresponding to the previous track for locations other than thelocation of the gap and includes data from a track preceding theprevious track at the location of the gap; and an inter-trackinterference determination circuit operable to calculate an inter-trackinterference from the previous track data set based at least in part onthe previous track data set and a current track data set.
 19. Thestorage device of claim 18, wherein the inter-track interferencedetermination circuit comprises: an inter-track interference responsecircuit operable to estimate an inter-track interference response fromthe previous track data set based at least in part on the previous trackdata set and a current track data set; and an inter-track interferencesignal estimator circuit operable to calculate an inter-trackinterference from the previous track data set based at least in part onthe previous track data set and the inter-track interference responsefrom the previous track data set.
 20. The storage device of claim 18,wherein the read channel circuit further comprises: an inter-trackinterference cancellation circuit operable to cancel the inter-trackinterference from the previous track data set to yield a compensatedoutput.